[Octave-cvsupdate] SF.net SVN: octave:[8436] trunk/octave-forge/main/control/devel

[<par...@us...>]

Revision: 8436
          http://octave.svn.sourceforge.net/octave/?rev=8436&view=rev
Author:   paramaniac
Date:     2011-08-05 16:25:50 +0000 (Fri, 05 Aug 2011)

Log Message:
-----------
control: add stuff for pdf manual

Added Paths:
-----------
    trunk/octave-forge/main/control/devel/pdfdoc/
    trunk/octave-forge/main/control/devel/pdfdoc/doc.tex
    trunk/octave-forge/main/control/devel/pdfdoc/function_doc.m
    trunk/octave-forge/main/control/devel/pdfdoc/functions.texi

Added: trunk/octave-forge/main/control/devel/pdfdoc/doc.tex
===================================================================
--- trunk/octave-forge/main/control/devel/pdfdoc/doc.tex	                        (rev 0)
+++ trunk/octave-forge/main/control/devel/pdfdoc/doc.tex	2011-08-05 16:25:50 UTC (rev 8436)
@@ -0,0 +1,11 @@
+\input texinfo   @c -*-texinfo-*-
+@c %**start of header
+@setfilename doc.info
+@settitle Sample Manual 1.0
+@c %**end of header
+
+@contents
+@chapter Function Reference
+@include functions.texi
+
+@end

Added: trunk/octave-forge/main/control/devel/pdfdoc/function_doc.m
===================================================================
--- trunk/octave-forge/main/control/devel/pdfdoc/function_doc.m	                        (rev 0)
+++ trunk/octave-forge/main/control/devel/pdfdoc/function_doc.m	2011-08-05 16:25:50 UTC (rev 8436)
@@ -0,0 +1,31 @@
+% pack_name = "generate_html"
+pack_name = "control"
+
+
+% Load Packages
+pkg load "generate_html"
+pkg ("load", pack_name);
+
+% Get list of functions  
+list = pkg ("describe", pack_name);
+
+%list
+
+% Open output file
+fid = fopen ("functions.texi", "w");
+
+for k = 1:numel (list {1}.provides)
+        
+        group = list {1}.provides{k};
+        functions = group.functions;
+
+        fprintf (fid, '@section %s\n', group.category);
+        
+        for k=1:numel(functions)
+                [TEXT, FORMAT] = get_help_text (functions(k));
+                fprintf (fid,TEXT);
+        end
+        
+end
+
+fclose(fid);
\ No newline at end of file

Added: trunk/octave-forge/main/control/devel/pdfdoc/functions.texi
===================================================================
--- trunk/octave-forge/main/control/devel/pdfdoc/functions.texi	                        (rev 0)
+++ trunk/octave-forge/main/control/devel/pdfdoc/functions.texi	2011-08-05 16:25:50 UTC (rev 8436)
@@ -0,0 +1,2342 @@
+@section Examples and Demos
+
+ @deftypefn{Function File} {@var{sys} =} BMWengine ()
+ @deftypefnx{Function File} {@var{sys} =} BMWengine (@var{"scaled"})
+ @deftypefnx{Function File} {@var{sys} =} BMWengine (@var{"unscaled"})
+ Model of the BMW 4-cylinder engine at ETH Zurich's control laboratory.
+ @example
+ @group
+ OPERATING POINT
+ Drosselklappenstellung     alpha_DK = 10.3 Grad
+ Saugrohrdruck              p_s = 0.48 bar
+ Motordrehzahl              n = 860 U/min
+ Lambda-Messwert            lambda = 1.000
+ Relativer Wandfilminhalt   nu = 1
+
+ INPUTS
+ U_1 Sollsignal Drosselklappenstellung   [Grad]
+ U_2 Relative Einspritzmenge             [-]
+ U_3 Zuendzeitpunkt                      [Grad KW]
+ M_L Lastdrehmoment                      [Nm]
+
+ STATES
+ X_1 Drosselklappenstellung     [Grad]
+ X_2 Saugrohrdruck              [bar]
+ X_3 Motordrehzahl              [U/min]
+ X_4 Messwert Lamba-Sonde       [-]
+ X_5 Relativer Wandfilminhalt   [-]
+
+ OUTPUTS
+ Y_1 Motordrehzahl              [U/min]    
+ Y_2 Messwert Lambda-Sonde      [-]
+
+ SCALING
+ U_1N, X_1N   1 Grad
+ U_2N, X_4N, X_5N, Y_2N   0.05
+ U_3N   1.6 Grad KW
+ X_2N   0.05 bar
+ X_3N, Y_1N   200 U/min
+ @end group
+ @end example
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} Boeing707 ()
+ Creates a linearized state-space model of a Boeing 707-321 aircraft
+ at @var{v}=80 m/s 
+ @iftex
+ @tex
+ ($M = 0.26$, $G_{a0} = -3^{circ}$, ${lpha}_0 = 4^{circ}$, ${kappa}= 50^{circ}$).
+ @end tex
+ @end iftex
+ @ifinfo
+ (@var{M} = 0.26, @var{Ga0} = -3 deg, @var{alpha0} = 4 deg, @var{kappa} = 50 deg).
+ @end ifinfo
+
+ System inputs: (1) thrust and (2) elevator angle.
+
+ System outputs:  (1) airspeed and (2) pitch angle.
+
+ @strong{Reference}: R. Brockhaus: @cite{Flugregelung} (Flight
+ Control), Springer, 1994.
+ @end deftypefn
+ ===============================================================================
+ optiPID                          Lukas Reichlin                       July 2009
+ ===============================================================================
+ Numerical Optimization of an A/H PID Controller
+ Required OCTAVE Packages: control, optim (and its dependencies)
+ Required MATLAB Toolboxes: Control, Optimization
+ ===============================================================================
+
+ @deftypefn{Function File} {@var{sys} =} WestlandLynx ()
+ Model of the Westland Lynx Helicopter about hover.
+ @example
+ @group
+ INPUTS
+ main rotor collective
+ longitudinal cyclic
+ lateral cyclic
+ tail rotor collective
+
+ STATES
+ pitch attitude           theta       [rad]
+ roll attitude            phi         [rad]
+ roll rate (body-axis)    p           [rad/s]
+ pitch rate (body-axis)   q           [rad/s]
+ yaw rate                 xi          [rad/s]
+ forward velocity         v_x         [ft/s]
+ lateral velocity         v_y         [ft/s]
+ vertical velocity        v_z         [ft/s]
+
+ OUTPUTS
+ heave velocity           H_dot       [ft/s]
+ pitch attitude           theta       [rad]
+ roll attitude            phi         [rad]
+ heading rate             psi_dot     [rad/s]
+ roll rate                p           [rad/s]
+ pitch rate               q           [rad/s]
+
+ Reference:
+ Skogestad, S. and Postlethwaite I.
+ Multivariable Feedback Control: Analysis and Design
+ Second Edition
+ Wiley 2005
+ http://www.nt.ntnu.no/users/skoge/book/2nd_edition/matlab_m/matfiles.html
+ @end group
+ @end example
+ @end deftypefn
+@section Linear Time Invariant Models
+
+ @deftypefn {Function File} {@var{sys} =} dss (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} dss (@var{d})
+ @deftypefnx {Function File} {@var{sys} =} dss (@var{a}, @var{b}, @var{c}, @var{d}, @var{e}, @dots{})
+ @deftypefnx {Function File} {@var{sys} =} dss (@var{a}, @var{b}, @var{c}, @var{d}, @var{e}, @var{tsam}, @dots{})
+ Create or convert to descriptor state-space model.
+
+ @strong{Inputs}
+ @table @var
+ @item a
+ State transition matrix (n-by-n).
+ @item b
+ Input matrix (n-by-m).
+ @item c
+ Measurement matrix (p-by-n).
+ @item d
+ Feedthrough matrix (p-by-m).
+ @item e
+ Descriptor matrix (n-by-n).
+ @item tsam
+ Sampling time in seconds.  If @var{tsam} is not specified, 
+ a continuous-time model is assumed.
+ @item @dots{}
+ Optional pairs of properties and values.
+ Type @command{set (dss)} for more information.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ Descriptor state-space model.
+ @end table
+
+ @strong{Equations}
+ @example
+ @group
+   .
+ E x = A x + B u
+   y = C x + D u
+ @end group
+ @end example
+
+ @seealso{ss, tf}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} frd (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} frd (@var{sys}, @var{w})
+ @deftypefnx {Function File} {@var{sys} =} frd (@var{H}, @var{w}, @dots{})
+ @deftypefnx {Function File} {@var{sys} =} frd (@var{H}, @var{w}, @var{tsam}, @dots{})
+ Create or convert to frequency response data.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.  If second argument @var{w} is omitted, the interesting
+ frequency range is calculated by the zeros and poles of @var{sys}.
+ @item H
+ Frequency response array (p-by-m-by-lw).  In the SISO case,
+ a vector (lw-by-1) or (1-by-lw) is accepted as well.
+ @item w
+ Frequency vector (lw-by-1) in radian per second [rad/s].
+ @item tsam
+ Sampling time in seconds.  If @var{tsam} is not specified,
+ a continuous-time model is assumed.
+ @item @dots{}
+ Optional pairs of properties and values.
+ Type @command{set (frd)} for more information.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ Frequency response data object.
+ @end table
+
+ @seealso{dss, ss, tf}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} ss (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} ss (@var{d})
+ @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b})
+ @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @var{c})
+ @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @var{c}, @var{d}, @dots{})
+ @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @dots{})
+ Create or convert to state-space model.
+
+ @strong{Inputs}
+ @table @var
+ @item a
+ State transition matrix (n-by-n).
+ @item b
+ Input matrix (n-by-m).
+ @item c
+ Measurement matrix (p-by-n).
+ If @var{c} is empty @code{[]} or not specified, an identity matrix is assumed.
+ @item d
+ Feedthrough matrix (p-by-m).
+ If @var{d} is empty @code{[]} or not specified, a zero matrix is assumed.
+ @item tsam
+ Sampling time in seconds.  If @var{tsam} is not specified, a continuous-time model is assumed.
+ @item @dots{}
+ Optional pairs of properties and values.
+ Type @command{set (ss)} for more information.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ State-space model.
+ @end table
+
+ @strong{Example}
+ @example
+ @group
+ octave:1> a = [1 2 3; 4 5 6; 7 8 9];
+ octave:2> b = [10; 11; 12];
+ octave:3> stname = @{"V", "A", "kJ"@};
+ octave:4> sys = ss (a, b, [], [], "stname", stname)
+ 
+ sys.a =
+         V   A  kJ
+    V    1   2   3
+    A    4   5   6
+    kJ   7   8   9
+ 
+ sys.b =
+        u1
+    V   10
+    A   11
+    kJ  12
+ 
+ sys.c =
+         V   A  kJ
+    y1   1   0   0
+    y2   0   1   0
+    y3   0   0   1
+ 
+ sys.d =
+        u1
+    y1   0
+    y2   0
+    y3   0
+ 
+ Continuous-time model.
+ octave:5> 
+ @end group
+ @end example
+
+ @seealso{tf, dss}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{s} =} tf (@var{"s"})
+ @deftypefnx {Function File} {@var{z} =} tf (@var{"z"}, @var{tsam})
+ @deftypefnx {Function File} {@var{sys} =} tf (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} tf (@var{num}, @var{den}, @dots{})
+ @deftypefnx {Function File} {@var{sys} =} tf (@var{num}, @var{den}, @var{tsam}, @dots{})
+ Create or convert to transfer function model.
+
+ @strong{Inputs}
+ @table @var
+ @item num
+ Numerator or cell of numerators.  Each numerator must be a row vector
+ containing the exponents of the polynomial in descending order.
+ @item den
+ Denominator or cell of denominators.  Each denominator must be a row vector
+ containing the exponents of the polynomial in descending order.
+ @item tsam
+ Sampling time in seconds.  If @var{tsam} is not specified, a continuous-time
+ model is assumed.
+ @item @dots{}
+ Optional pairs of properties and values.
+ Type @command{set (tf)} for more information.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ Transfer function model.
+ @end table
+
+ @strong{Example}
+ @example
+ @group
+ octave:1> s = tf ("s");
+ octave:2> G = 1/(s+1)
+
+ Transfer function "G" from input "u1" to output ...
+         1  
+  y1:  -----
+       s + 1
+
+ octave:3> z = tf ("z", 0.2);
+ octave:4> H = 0.095/(z-0.9)
+ 
+ Transfer function "H" from input "u1" to output ...
+        0.095 
+  y1:  -------
+       z - 0.9
+ 
+ Sampling time: 0.2 s
+ octave:5> 
+ @end group
+ @end example
+
+ @seealso{ss, dss}
+ @end deftypefn
+@section Model Data Access
+
+ @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}, @var{e}, @var{tsam}] =} dssdata (@var{sys})
+ @deftypefnx {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}, @var{e}, @var{tsam}] =} dssdata (@var{sys}, @var{[]})
+ Access descriptor state-space model data.
+ Argument @var{sys} is not limited to descriptor state-space models.
+ If @var{sys} is not a descriptor state-space model, it is converted automatically.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ Any type of LTI model.
+ @item []
+ In case @var{sys} is not a dss model (descriptor matrix @var{e} empty),
+ @code{dssdata (sys, [])} returns the empty element @code{e = []} whereas
+ @code{dssdata (sys)} returns the identity matrix @code{e = eye (size (a))}.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item a
+ State transition matrix (n-by-n).
+ @item b
+ Input matrix (n-by-m).
+ @item c
+ Measurement matrix (p-by-n).
+ @item d
+ Feedthrough matrix (p-by-m).
+ @item e
+ Descriptor matrix (n-by-n).
+ @item tsam
+ Sampling time in seconds.  If @var{sys} is a continuous-time model,
+ a zero is returned.
+ @end table
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{H}, @var{w}, @var{tsam}] =} frdata (@var{sys})
+ @deftypefnx {Function File} {[@var{H}, @var{w}, @var{tsam}] =} frdata (@var{sys}, @var{"vector"})
+ Access frequency response data.
+ Argument @var{sys} is not limited to frequency response data objects.
+ If @var{sys} is not a frd object, it is converted automatically.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ Any type of LTI model.
+ @item "v", "vector"
+ In case @var{sys} is a SISO model, this option returns the frequency response
+ as a column vector (lw-by-1) instead of an array (p-by-m-by-lw).
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item H
+ Frequency response array (p-by-m-by-lw).  In the SISO case,
+ a vector (lw-by-1) is possible as well.
+ @item w
+ Frequency vector (lw-by-1) in radian per second [rad/s].
+ @item tsam
+ Sampling time in seconds.  If @var{sys} is a continuous-time model,
+ a zero is returned.
+ @end table
+ @end deftypefn
+
+ @deftypefn {Function File} get (@var{sys})
+ @deftypefnx {Function File} {@var{value} =} get (@var{sys}, @var{"property"})
+ Access property values of LTI objects.
+ @end deftypefn
+
+ @deftypefn {Function File} set (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} set (@var{sys}, @var{"property"}, @var{value})
+ Set or modify properties of LTI objects.
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}] =} ssdata (@var{sys})
+ Access state-space model data.
+ Argument @var{sys} is not limited to state-space models.
+ If @var{sys} is not a state-space model, it is converted automatically.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ Any type of LTI model.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item a
+ State transition matrix (n-by-n).
+ @item b
+ Input matrix (n-by-m).
+ @item c
+ Measurement matrix (p-by-n).
+ @item d
+ Feedthrough matrix (p-by-m).
+ @item tsam
+ Sampling time in seconds.  If @var{sys} is a continuous-time model,
+ a zero is returned.
+ @end table
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{num}, @var{den}, @var{tsam}] =} tfdata (@var{sys})
+ @deftypefnx {Function File} {[@var{num}, @var{den}, @var{tsam}] =} tfdata (@var{sys}, @var{"tfpoly"})
+ Access transfer function data.
+ @end deftypefn
+@section Model Conversions
+
+ @deftypefn {Function File} {@var{sys} =} c2d (@var{sys}, @var{tsam})
+ @deftypefnx {Function File} {@var{sys} =} c2d (@var{sys}, @var{tsam}, @var{method})
+ Convert the continuous lti model into its discrete time equivalent.
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{scaledsys}, @var{info}] =} prescale (@var{sys})
+ Prescale state-space model.
+ Uses SLICOT TB01ID and TG01AD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}.
+ Frequency response commands perform automatic scaling unless model property
+ @var{scaled} is set to @var{true}.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item scaledsys
+ Scaled state-space model.
+ @item info
+ Structure containing additional information.
+ @item info.SL
+ Left scaling factors.  @code{Tl = diag (info.SL)}.
+ @item info.SR
+ Right scaling factors.  @code{Tr = diag (info.SR)}.
+ @end table
+
+ @strong{Equations}
+ @example
+ @group
+ Es = Tl E Tr
+ As = Tl A Tr
+ Bs = Tl B
+ Cs =    C Tr
+ Ds =    D
+
+ For proper state-space models, Tl and Tr are inverse of each other.
+ @end group
+ @end example
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} xperm (@var{sys}, @var{st_idx})
+ Reorder states in state-space models.
+ @end deftypefn
+@section Model Interconnections
+
+ @deftypefn {Function File} {@var{sys} =} append (@var{sys1}, @var{sys2})
+ Group LTI models by appending their inputs and outputs.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} blkdiag (@var{sys1}, @var{sys2})
+ Block-diagonal concatenation of LTI models.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} connect (@var{sys}, @var{cm}, @var{inputs}, @var{outputs})
+ Arbitrary interconnections between the inputs and outputs of an LTI model.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} feedback (@var{sys1})
+ @deftypefnx {Function File} {@var{sys} =} feedback (@var{sys1}, @var{"+"})
+ @deftypefnx {Function File} {@var{sys} =} feedback (@var{sys1}, @var{sys2})
+ @deftypefnx {Function File} {@var{sys} =} feedback (@var{sys1}, @var{sys2}, @var{"+"})
+ @deftypefnx {Function File} {@var{sys} =} feedback (@var{sys1}, @var{sys2}, @var{feedin}, @var{feedout})
+ @deftypefnx {Function File} {@var{sys} =} feedback (@var{sys1}, @var{sys2}, @var{feedin}, @var{feedout}, @var{"+"})
+ Feedback connection of two LTI models.
+
+ @strong{Block Diagram}
+ @example
+ @group
+  u    +         +--------+             y
+ ------>(+)----->|  sys1  |-------+------->
+         ^ -     +--------+       |
+         |                        |
+         |       +--------+       |
+         +-------|  sys2  |<------+
+                 +--------+
+ @end group
+ @end example
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} lft (@var{sys1}, @var{sys2})
+ @deftypefnx {Function File} {@var{sys} =} lft (@var{sys1}, @var{sys2}, @var{nu}, @var{ny})
+ Linear fractional tranformation, also known as Redheffer star product.
+
+ @strong{Inputs}
+ @table @var
+ @item sys1
+ Upper LTI model.
+ @item sys2
+ Lower LTI model.
+ @item nu
+ The last nu inputs of @var{sys1} are connected with the first nu outputs of @var{sys2}.
+ If not specified, @code{min (m1, p2)} is taken.
+ @item ny
+ The last ny outputs of @var{sys1} are connected with the first ny inputs of @var{sys2}.
+ If not specified, @code{min (p1, m2)} is taken.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ Resulting LTI model.
+ @end table
+
+ @strong{Block Diagram}
+ @example
+ @group
+       .............sys..............
+       :         +--------+         :
+ w1 ------------>|        |------------> z1
+       :         |  sys1  |         :
+       : u +---->|        |-----+ y :
+       :   |     +--------+     |   :          Lower LFT
+       :   |                    |   :
+       :   |     +--------+     |   :          lft (sys1, sys2)
+       :   +-----|  sys2  |<----+   :
+       :         +--------+         :
+       :............................:
+
+
+       .............sys..............
+       :         +--------+         :
+       : u +---->|  sys1  |-----+ y :
+       :   |     +--------+     |   :          Upper LFT
+       :   |                    |   :
+       :   |     +--------+     |   :          lft (sys1, sys2)
+       :   +-----|        |<----+   :
+       :         |  sys2  |         :
+ z2 <------------|        |<------------ w2
+       :         +--------+         :
+       :............................:
+
+
+       .............sys..............
+       :         +--------+         :
+ w1 ------------>|        |------------> z1
+       :         |  sys1  |         :
+       : u +---->|        |-----+ y :
+       :   |     +--------+     |   :
+       :   |                    |   :          lft (sys1, sys2, nu, ny)
+       :   |     +--------+     |   :
+       :   +-----|        |<----+   :
+       :         |  sys2  |         :
+ z2 <------------|        |<------------ w2
+       :         +--------+         :
+       :............................: 
+ @end group
+ @end example
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} mconnect (@var{sys}, @var{m})
+ @deftypefnx {Function File} {@var{sys} =} mconnect (@var{sys}, @var{m}, @var{inputs}, @var{outputs})
+ Arbitrary interconnections between the inputs and outputs of an LTI model.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.
+ @item m
+ Connection matrix.  Each row belongs to an input and each column represents an output.
+ @item inputs
+ Vector of indices of those inputs which are retained.  If not specified, all inputs are kept.
+ @item outputs
+ Vector of indices of those outputs which are retained.  If not specified, all outputs are kept.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ Interconnected system.
+ @end table
+
+ @strong{Example}
+ @example
+ @group
+ Solve the system equations of
+ y(t) = G e(t)
+ e(t) = u(t) + M y(t)
+ in order to build
+ y(t) = H u(t)
+ The matrix M for a (p-by-m) system G
+ has m rows and p columns (m-by-p).
+
+ Example for a 3x2 system:
+ u1 = -1*y1 + 5*y2 + 0*y3
+ u2 = pi*y1 + 0*y2 - 7*y3
+
+     | -1      5      0 |
+ M = | pi      0      7 |
+ @end group
+ @end example
+ @end deftypefn
+
+ @deftypefn{Function File} {@var{sys} =} parallel (@var{sys1}, @var{sys2})
+ Parallel connection of two LTI systems.
+
+ @strong{Block Diagram}
+ @example
+ @group
+     ..........................
+     :      +--------+        :
+     :  +-->|  sys1  |---+    :
+  u  :  |   +--------+   | +  :  y
+ -------+                O--------->
+     :  |   +--------+   | +  :
+     :  +-->|  sys2  |---+    :
+     :      +--------+        :
+     :.........sys............:
+
+ sys = parallel (sys1, sys2)
+ @end group
+ @end example
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} series (@var{sys1}, @var{sys2})
+ @deftypefnx {Function File} {@var{sys} =} series (@var{sys1}, @var{sys2}, @var{outputs1}, @var{inputs2})
+ Series connection of two LTI models.
+
+ @strong{Block Diagram}
+ @example
+ @group
+     .....................................
+  u  :  +--------+ y1    u2  +--------+  :  y
+ ------>|  sys1  |---------->|  sys2  |------->
+     :  +--------+           +--------+  :
+     :................sys.................
+
+ sys = series (sys1, sys2)
+
+
+     .....................................
+     :                   v2  +--------+  :
+     :            ---------->|        |  :  y
+     :  +--------+ y1    u2  |  sys2  |------->
+  u  :  |        |---------->|        |  :
+ ------>|  sys1  |       z1  +--------+  :
+     :  |        |---------->            :
+     :  +--------+                       :
+     :................sys.................
+
+ outputs1 = [1]
+ inputs2 = [2]
+ sys = series (sys1, sys2, outputs1, inputs2)
+ @end group
+ @end example
+ @end deftypefn
+@section Model Characteristics
+
+ @deftypefn {Function File} {@var{co} =} ctrb (@var{sys})
+ @deftypefnx {Function File} {@var{co} =} ctrb (@var{a}, @var{b})
+ Controllability matrix.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{k} =} dcgain (@var{sys})
+ DC gain of LTI model.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item k
+ DC gain matrice.  For a system with m inputs and p outputs, the array @var{k}
+ has dimensions [p, m].
+ @end table
+
+ @seealso{freqresp}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{W} =} gram (@var{sys}, @var{mode})
+ @deftypefnx {Function File} {@var{Wc} =} gram (@var{a}, @var{b})
+ @code{gram (@var{sys}, "c")} returns the controllability gramian of
+ the (continuous- or discrete-time) system @var{sys}.
+ @code{gram (@var{sys}, "o")} returns the observability gramian of the
+ (continuous- or discrete-time) system @var{sys}.
+ @code{gram (@var{a}, @var{b})} returns the controllability gramian
+ @var{Wc} of the continuous-time system @math{dx/dt = a x + b u};
+ i.e., @var{Wc} satisfies @math{a Wc + m Wc' + b b' = 0}.
+
+ @end deftypefn
+
+ @deftypefn{Function File} {@var{hsv} =} hsvd (@var{sys})
+ @deftypefnx{Function File} {@var{hsv} =} hsvd (@var{sys}, @var{"offset"}, @var{alpha})
+ Hankel singular values of the stable part of an LTI model.  If no output arguments are
+ given, the Hankel singular values are displayed in a plot.
+ Uses SLICOT AB13AD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isct (@var{sys})
+ Determine whether LTI model is a continuous-time system.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isctrb (@var{sys})
+ @deftypefnx {Function File} {@var{bool} =} isctrb (@var{sys}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isctrb (@var{a}, @var{b})
+ @deftypefnx {Function File} {@var{bool} =} isctrb (@var{a}, @var{b}, @var{e})
+ @deftypefnx {Function File} {@var{bool} =} isctrb (@var{a}, @var{b}, @var{[]}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isctrb (@var{a}, @var{b}, @var{e}, @var{tol})
+ Logical check for system controllability.
+ Uses SLICOT AB01OD and TG01HD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @item a
+ State transition matrix.
+ @item b
+ Input matrix.
+ @item e
+ Descriptor matrix.
+ @item tol
+ Optional roundoff parameter.  Default value is 0.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item bool = 0
+ System is not controllable.
+ @item bool = 1
+ System is controllable.
+ @end table
+
+ @seealso{isobsv}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isdetectable (@var{sys})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{sys}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{e})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{[]}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{e}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{[]}, @var{[]}, @var{dflg})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{e}, @var{[]}, @var{dflg})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{[]}, @var{tol}, @var{dflg})
+ @deftypefnx {Function File} {@var{bool} =} isdetectable (@var{a}, @var{c}, @var{e}, @var{tol}, @var{dflg})
+ Logical test for system detectability.
+ All unstable modes must be observable or all unobservable states must be stable.
+ Uses SLICOT AB01OD and TG01HD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.
+ @item a
+ State transition matrix.
+ @item c
+ Measurement matrix.
+ @item e
+ Descriptor matrix.
+ @item tol
+ Optional tolerance for stability.  Default value is 0.
+ @item dflg = 0
+ Matrices (@var{a}, @var{c}) are part of a continuous-time system.  Default Value.
+ @item dflg = 1
+ Matrices (@var{a}, @var{c}) are part of a discrete-time system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item bool = 0
+ System is not detectable.
+ @item bool = 1
+ System is detectable.
+ @end table
+
+ See @command{isstabilizable} for description of computational method.
+ @seealso{isstabilizable, isstable, isctrb, isobsv}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isdt (@var{sys})
+ Determine whether LTI model is a discrete-time system.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isminimumphase (@var{sys})
+ @deftypefnx {Function File} {@var{bool} =} isminimumphase (@var{sys}, @var{tol})
+ Determine whether LTI system is minimum phase.
+ If a square system @var{P} is minimum-phase, its inverse @var{P^-1} is stable.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isobsv (@var{sys})
+ @deftypefnx {Function File} {@var{bool} =} isobsv (@var{sys}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isobsv (@var{a}, @var{c})
+ @deftypefnx {Function File} {@var{bool} =} isobsv (@var{a}, @var{c}, @var{e})
+ @deftypefnx {Function File} {@var{bool} =} isobsv (@var{a}, @var{c}, @var{[]}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isobsv (@var{a}, @var{c}, @var{e}, @var{tol})
+ Logical check for system observability.
+ Uses SLICOT AB01OD and TG01HD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @item a
+ State transition matrix.
+ @item c
+ Measurement matrix.
+ @item e
+ Descriptor matrix.
+ @item tol
+ Optional roundoff parameter.  Default value is 0.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item bool = 0
+ System is not observable.
+ @item bool = 1
+ System is observable.
+ @end table
+
+ @seealso{isctrb}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} issiso (@var{sys})
+ Determine whether LTI model is single-input/single-output (SISO).
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isstabilizable (@var{sys})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{sys}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{[]}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e}, @var{tol})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{[]}, @var{[]}, @var{dflg})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e}, @var{[]}, @var{dflg})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{[]}, @var{tol}, @var{dflg})
+ @deftypefnx {Function File} {@var{bool} =} isstabilizable (@var{a}, @var{b}, @var{e}, @var{tol}, @var{dflg})
+ Logical check for system stabilizability.
+ All unstable modes must be controllable or all uncontrollable states must be stable.
+ Uses SLICOT AB01OD and TG01HD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.
+ @item a
+ State transition matrix.
+ @item b
+ Input matrix.
+ @item e
+ Descriptor matrix.
+ @item tol
+ Optional tolerance for stability.  Default value is 0.
+ @item dflg = 0
+ Matrices (@var{a}, @var{b}) are part of a continuous-time system.  Default Value.
+ @item dflg = 1
+ Matrices (@var{a}, @var{b}) are part of a discrete-time system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item bool = 0
+ System is not stabilizable.
+ @item bool = 1
+ System is stabilizable.
+ @end table
+
+ @strong{Method}
+ @example
+ @group
+ * Calculate staircase form (SLICOT AB01OD)
+ * Extract unobservable part of state transition matrix
+ * Calculate eigenvalues of unobservable part
+ * Check whether
+   real (ev) < -tol*(1 + abs (ev))   continuous-time
+   abs (ev) < 1 - tol                discrete-time
+ @end group
+ @end example
+ @seealso{isdetectable, isstable, isctrb, isobsv}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{bool} =} isstable (@var{sys})
+ @deftypefnx {Function File} {@var{bool} =} isstable (@var{sys}, @var{tol})
+ Determine whether LTI system is stable.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{gain} =} norm (@var{sys}, @var{2})
+ @deftypefnx {Function File} {[@var{gain}, @var{wpeak}] =} norm (@var{sys}, @var{inf})
+ @deftypefnx {Function File} {[@var{gain}, @var{wpeak}] =} norm (@var{sys}, @var{inf}, @var{tol})
+ Return H-2 or L-inf norm of LTI model.
+ Uses SLICOT AB13BD and AB13DD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{ob} =} obsv (@var{sys})
+ @deftypefnx {Function File} {@var{ob} =} obsv (@var{a}, @var{c})
+ Observability matrix.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{p} =} pole (@var{sys})
+ Compute poles of LTI system.
+ @end deftypefn
+
+ @deftypefn {Function File} pzmap (@var{sys})
+ @deftypefnx {Function File} {[@var{p}, @var{z}] =} pzmap (@var{sys})
+ Plot the poles and zeros of an LTI system in the complex plane.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{nvec} =} size (@var{ltisys})
+ @deftypefnx {Function File} {@var{n} =} size (@var{ltisys}, @var{idx})
+ @deftypefnx {Function File} {[@var{ny}, @var{nu}] =} size (@var{ltisys})
+ LTI model size, i.e. number of outputs and inputs.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{z} =} zero (@var{sys})
+ @deftypefnx {Function File} {[@var{z}, @var{k}] =} zero (@var{sys})
+ Compute transmission zeros and gain of LTI model.
+ @end deftypefn
+@section Model Simplification
+
+ @deftypefn {Function File} {@var{sys} =} minreal (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} minreal (@var{sys}, @var{tol})
+ Minimal realization or zero-pole cancellation of LTI models.
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{sys} =} sminreal (@var{sys})
+ @deftypefnx {Function File} {@var{sys} =} sminreal (@var{sys}, @var{tol})
+ Perform state-space model reduction based on structure.
+ Remove states which have no influence on the input-output behaviour.
+ The physical meaning of the states is retained.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ State-space model.
+ @item tol
+ Optional tolerance for controllability and observability. 
+ Entries of the state-space matrices whose moduli are less or equal to @var{tol}
+ are assumed to be zero.  Default value is 0.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sys
+ Reduced state-space model.
+ @end table
+
+ @seealso{minreal}
+ @end deftypefn
+@section Time Domain Analysis
+
+ @deftypefn{Function File} {[@var{p}, @var{q}] =} covar (@var{sys}, @var{w})
+ Return the steady-state covariance.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @item w
+ Intensity of white noise inputs which drive @var{sys}.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item p
+ Output covariance.
+ @item q
+ State covariance.
+ @end table
+
+ @seealso{lyap, dlyap}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{u}, @var{t}] =} gensig (@var{sigtype}, @var{tau})
+ @deftypefnx{Function File} {[@var{u}, @var{t}] =} gensig (@var{sigtype}, @var{tau}, @var{tfinal})
+ @deftypefnx{Function File} {[@var{u}, @var{t}] =} gensig (@var{sigtype}, @var{tau}, @var{tfinal}, @var{tsam})
+ Generate periodic signal.  Useful in combination with lsim.
+
+ @strong{Inputs}
+ @table @var
+ @item sigtype = "sin"
+ Sine wave.
+ @item sigtype = "cos"
+ Cosine wave.
+ @item sigtype = "square"
+ Square wave.
+ @item sigtype = "pulse"
+ Periodic pulse.
+ @item tau
+ Duration of one period in seconds.
+ @item tfinal
+ Optional duration of the signal in seconds.  Default duration is 5 periods.
+ @item tsam
+ Optional sampling time in seconds.  Default spacing is tau/64.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item u
+ Vector of signal values.
+ @item t
+ Time vector of the signal.
+ @end table
+
+ @seealso{lsim}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{y}, @var{t}, @var{x}] =} impulse (@var{sys})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} impulse (@var{sys}, @var{t})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} impulse (@var{sys}, @var{tfinal})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} impulse (@var{sys}, @var{tfinal}, @var{dt})
+ Impulse response of LTI system.
+ If no output arguments are given, the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @item t
+ Time vector.  Should be evenly spaced.  If not specified, it is calculated by
+ the poles of the system to reflect adequately the response transients.
+ @item tfinal
+ Optional simulation horizon.  If not specified, it is calculated by
+ the poles of the system to reflect adequately the response transients.
+ @item dt
+ Optional sampling time.  Be sure to choose it small enough to capture transient
+ phenomena.  If not specified, it is calculated by the poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item y
+ Output response array.  Has as many rows as time samples (length of t)
+ and as many columns as outputs.
+ @item t
+ Time row vector.
+ @item x
+ State trajectories array.  Has @code{length (t)} rows and as many columns as states.
+ @end table
+
+ @seealso{initial, lsim, step}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{t})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{tfinal})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} initial (@var{sys}, @var{x0}, @var{tfinal}, @var{dt})
+ Initial condition response of state-space model.
+ If no output arguments are given, the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ State-space model.
+ @item x0
+ Vector of initial conditions for each state.
+ @item t
+ Optional time vector.  Should be evenly spaced.  If not specified, it is calculated
+ by the poles of the system to reflect adequately the response transients.
+ @item tfinal
+ Optional simulation horizon.  If not specified, it is calculated by
+ the poles of the system to reflect adequately the response transients.
+ @item dt
+ Optional sampling time.  Be sure to choose it small enough to capture transient
+ phenomena.  If not specified, it is calculated by the poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item y
+ Output response array.  Has as many rows as time samples (length of t)
+ and as many columns as outputs.
+ @item t
+ Time row vector.
+ @item x
+ State trajectories array.  Has @code{length (t)} rows and as many columns as states.
+ @end table
+
+ @strong{Example}
+ @example
+ @group
+                    .
+ Continuous Time:   x = A x ,   y = C x ,   x(0) = x0
+
+ Discrete Time:   x[k+1] = A x[k] ,   y[k] = C x[k] ,   x[0] = x0
+ @end group
+ @end example
+
+ @seealso{impulse, lsim, step}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{[]}, @var{method})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0}, @var{method})
+ Simulate LTI model response to arbitrary inputs.  If no output arguments are given,
+ the system response is plotted on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.  System must be proper, i.e. it must not have more zeros than poles.
+ @item u
+ Vector or array of input signal.  Needs @code{length(t)} rows and as many columns
+ as there are inputs.  If @var{sys} is a single-input system, row vectors @var{u}
+ of length @code{length(t)} are accepted as well.
+ @item t
+ Time vector.  Should be evenly spaced.  If @var{sys} is a continuous-time system
+ and @var{t} is a real scalar, @var{sys} is discretized with sampling time
+ @code{tsam = t/(rows(u)-1)}.  If @var{sys} is a discrete-time system and @var{t}
+ is not specified, vector @var{t} is assumed to be @code{0 : tsam : tsam*(rows(u)-1)}.
+ @item x0
+ Vector of initial conditions for each state.  If not specified, a zero vector is assumed.
+ @item method
+ Discretization method for continuous-time models.  Default value is zoh
+ (zero-order hold).  All methods from @code{c2d} are supported. 
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item y
+ Output response array.  Has as many rows as time samples (length of t)
+ and as many columns as outputs.
+ @item t
+ Time row vector.  It is always evenly spaced.
+ @item x
+ State trajectories array.  Has @code{length (t)} rows and as many columns as states.
+ @end table
+
+ @seealso{impulse, initial, step}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{y}, @var{t}, @var{x}] =} step (@var{sys})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} step (@var{sys}, @var{t})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} step (@var{sys}, @var{tfinal})
+ @deftypefnx{Function File} {[@var{y}, @var{t}, @var{x}] =} step (@var{sys}, @var{tfinal}, @var{dt})
+ Step response of LTI system.
+ If no output arguments are given, the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @item t
+ Time vector.  Should be evenly spaced.  If not specified, it is calculated by
+ the poles of the system to reflect adequately the response transients.
+ @item tfinal
+ Optional simulation horizon.  If not specified, it is calculated by
+ the poles of the system to reflect adequately the response transients.
+ @item dt
+ Optional sampling time.  Be sure to choose it small enough to capture transient
+ phenomena.  If not specified, it is calculated by the poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item y
+ Output response array.  Has as many rows as time samples (length of t)
+ and as many columns as outputs.
+ @item t
+ Time row vector.
+ @item x
+ State trajectories array.  Has @code{length (t)} rows and as many columns as states.
+ @end table
+
+ @seealso{impulse, initial, lsim}
+ @end deftypefn
+@section Frequency Domain Analysis
+
+ @deftypefn {Function File} {[@var{mag}, @var{pha}, @var{w}] =} bode (@var{sys})
+ @deftypefnx {Function File} {[@var{mag}, @var{pha}, @var{w}] =} bode (@var{sys}, @var{w})
+ Bode diagram of frequency response.  If no output arguments are given,
+ the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.  Must be a single-input and single-output (SISO) system.
+ @item w
+ Optional vector of frequency values.  If @var{w} is not specified,
+ it is calculated by the zeros and poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item mag
+ Vector of magnitude.  Has length of frequency vector @var{w}.
+ @item pha
+ Vector of phase.  Has length of frequency vector @var{w}.
+ @item w
+ Vector of frequency values used.
+ @end table
+
+ @seealso{nichols, nyquist, sigma}
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{mag}, @var{w}] =} bodemag (@var{sys})
+ @deftypefnx {Function File} {[@var{mag}, @var{w}] =} bodemag (@var{sys}, @var{w})
+ Bode magnitude diagram of frequency response.  If no output arguments are given,
+ the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.  Must be a single-input and single-output (SISO) system.
+ @item w
+ Optional vector of frequency values.  If @var{w} is not specified,
+ it is calculated by the zeros and poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item mag
+ Vector of magnitude.  Has length of frequency vector @var{w}.
+ @item w
+ Vector of frequency values used.
+ @end table
+
+ @seealso{bode, nichols, nyquist, sigma}
+ @end deftypefn
+
+ @deftypefn{Function File} {@var{H} =} freqresp (@var{sys}, @var{w})
+ Evaluate frequency response at given frequencies.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.
+ @item w
+ Vector of frequency values.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item H
+ Array of frequency response.  For a system with m inputs and p outputs, the array @var{H}
+ has dimensions [p, m, length (w)].
+ The frequency response at the frequency w(k) is given by H(:,:,k).
+ @end table
+
+ @seealso{dcgain}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{gamma}, @var{phi}, @var{w_gamma}, @var{w_phi}] =} margin (@var{sys})
+ @deftypefnx{Function File} {[@var{gamma}, @var{phi}, @var{w_gamma}, @var{w_phi}] =} margin (@var{sys}, @var{tol})
+ Gain and phase margin of a system.  If no output arguments are given, both gain and phase margin
+ are plotted on a bode diagram.  Otherwise, the margins and their corresponding frequencies are
+ computed and returned.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.  Must be a single-input and single-output (SISO) system.
+ @item tol
+ Imaginary parts below @var{tol} are assumed to be zero.
+ If not specified, default value @code{sqrt (eps)} is taken.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item gamma
+ Gain margin (as gain, not dBs).
+ @item phi
+ Phase margin (in degrees).
+ @item w_gamma
+ Frequency for the gain margin (in rad/s).
+ @item w_phi
+ Frequency for the phase margin (in rad/s).
+ @end table
+
+ @strong{Equations}
+ @example
+ @group
+ CONTINUOUS SYSTEMS
+ Gain Margin
+         _               _
+ L(jw) = L(jw)      BTW: L(jw) = L(-jw) = conj (L(jw))
+
+ num(jw)   num(-jw)
+ ------- = --------
+ den(jw)   den(-jw)
+
+ num(jw) den(-jw) = num(-jw) den(jw)
+
+ imag (num(jw) den(-jw)) = 0
+ imag (num(-jw) den(jw)) = 0
+
+ Phase Margin
+           |num(jw)|
+ |L(jw)| = |-------| = 1
+           |den(jw)|
+   _     2      2
+ z z = Re z + Im z
+
+ num(jw)   num(-jw)
+ ------- * -------- = 1
+ den(jw)   den(-jw)
+
+ num(jw) num(-jw) - den(jw) den(-jw) = 0
+
+ real (num(jw) num(-jw) - den(jw) den(-jw)) = 0
+
+
+ DISCRETE SYSTEMS
+ Gain Margin
+                              jwT         log z
+ L(z) = L(1/z)      BTW: z = e    --> w = -----
+                                           j T
+ num(z)   num(1/z)
+ ------ = --------
+ den(z)   den(1/z)
+
+ num(z) den(1/z) - num(1/z) den(z) = 0
+
+ Phase Margin
+          |num(z)|
+ |L(z)| = |------| = 1
+          |den(z)|
+
+ L(z) L(1/z) = 1
+
+ num(z)   num(1/z)
+ ------ * -------- = 1
+ den(z)   den(1/z)
+
+ num(z) num(1/z) - den(z) den(1/z) = 0
+
+ PS: How to get L(1/z)
+           4       3       2
+ p(z) = a z  +  b z  +  c z  +  d z  +  e
+
+             -4      -3      -2      -1
+ p(1/z) = a z  +  b z  +  c z  +  d z  +  e
+
+           -4                    2       3       4
+        = z   ( a  +  b z  +  c z  +  d z  +  e z  )
+
+               4       3       2                     4
+        = ( e z  +  d z  +  c z  +  b z  +  a ) / ( z  )
+ @end group
+ @end example
+
+ @seealso{roots}
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{mag}, @var{pha}, @var{w}] =} nichols (@var{sys})
+ @deftypefnx {Function File} {[@var{mag}, @var{pha}, @var{w}] =} nichols (@var{sys}, @var{w})
+ Nichols chart of frequency response.  If no output arguments are given,
+ the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.  Must be a single-input and single-output (SISO) system.
+ @item w
+ Optional vector of frequency values.  If @var{w} is not specified,
+ it is calculated by the zeros and poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item mag
+ Vector of magnitude.  Has length of frequency vector @var{w}.
+ @item pha
+ Vector of phase.  Has length of frequency vector @var{w}.
+ @item w
+ Vector of frequency values used.
+ @end table
+
+ @seealso{bode, nyquist, sigma}
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{re}, @var{im}, @var{w}] =} nyquist (@var{sys})
+ @deftypefnx {Function File} {[@var{re}, @var{im}, @var{w}] =} nyquist (@var{sys}, @var{w})
+ Nyquist diagram of frequency response.  If no output arguments are given,
+ the response is printed on the screen.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.  Must be a single-input and single-output (SISO) system.
+ @item w
+ Optional vector of frequency values.  If @var{w} is not specified,
+ it is calculated by the zeros and poles of the system.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item re
+ Vector of real parts.  Has length of frequency vector @var{w}.
+ @item im
+ Vector of imaginary parts.  Has length of frequency vector @var{w}.
+ @item w
+ Vector of frequency values used.
+ @end table
+
+ @seealso{bode, nichols, sigma}
+ @end deftypefn
+
+ @deftypefn{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys})
+ @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{w})
+ @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{[]}, @var{ptype})
+ @deftypefnx{Function File} {[@var{sv}, @var{w}] =} sigma (@var{sys}, @var{w}, @var{ptype})
+ Singular values of frequency response.  If no output arguments are given,
+ the singular value plot is printed on the screen;
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.  Multiple inputs and/or outputs (MIMO systems) make practical sense.
+ @item w
+ Optional vector of frequency values.  If @var{w} is not specified,
+ it is calculated by the zeros and poles of the system.
+ @item ptype = 0
+ Singular values of the frequency response @var{H} of system @var{sys}.  Default Value.
+ @item ptype = 1
+ Singular values of the frequency response @code{inv(H)}; i.e. inversed system.
+ @item ptype = 2
+ Singular values of the frequency response @code{I + H}; i.e. inversed sensitivity
+ (or return difference) if @code{H = P * C}.
+ @item ptype = 3
+ Singular values of the frequency response @code{I + inv(H)}; i.e. inversed complementary
+ sensitivity if @code{H = P * C}.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item sv
+ Array of singular values.  For a system with m inputs and p outputs, the array sv
+ has @code{min (m, p)} rows and as many columns as frequency points @code{length (w)}.
+ The singular values at the frequency @code{w(k)} are given by @code{sv(:,k)}.
+ @item w
+ Vector of frequency values used.
+ @end table
+
+ @seealso{bodemag, svd}
+ @end deftypefn
+@section Pole Placement
+
+ @deftypefn {Function File} {@var{f} =} place (@var{sys}, @var{p})
+ @deftypefnx {Function File} {@var{f} =} place (@var{a}, @var{b}, @var{p})
+ @deftypefnx {Function File} {[@var{f}, @var{nfp}, @var{nap}, @var{nup}] =} place (@var{sys}, @var{p}, @var{alpha})
+ @deftypefnx {Function File} {[@var{f}, @var{nfp}, @var{nap}, @var{nup}] =} place (@var{a}, @var{b}, @var{p}, @var{alpha})
+ Pole assignment for a given matrix pair (@var{A},@var{B}) such that @code{p = eig (A-B*F)}.
+ If parameter @var{alpha} is specified, poles with real parts (continuous-time)
+ or moduli (discrete-time) below @var{alpha} are left untouched.
+ Uses SLICOT SB01BD by courtesy of
+ @uref{http://www.slicot.org, NICONET e.V.}
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI system.
+ @item a
+ State transition matrix (n-by-n) of a continuous-time system.
+ @item b
+ Input matrix (n-by-m) of a continuous-time system.
+ @item p
+ Desired eigenvalues of the closed-loop system state-matrix @var{A-B*F}.
+ @code{length (p) <= rows (A)}.
+ @item alpha
+ Specifies the maximum admissible value, either for real
+ parts or for moduli, of the eigenvalues of @var{A} which will
+ not be modified by the eigenvalue assignment algorithm.
+ @code{alpha >= 0} for discrete-time systems.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item f
+ State feedback gain matrix.
+ @item nfp
+ The number of fixed poles, i.e. eigenvalues of @var{A} having
+ real parts less than @var{alpha}, or moduli less than @var{alpha}.
+ These eigenvalues are not modified by @command{place}.
+ @item nap
+ The number of assigned eigenvalues.  @code{nap = n-nfp-nup}.
+ @item nup
+ The number of uncontrollable eigenvalues detected by the
+ eigenvalue assignment algorithm.
+ @end table
+
+ @strong{Note}
+ @example
+ Place is also suitable to design estimator gains:
+ @group
+ L = place (A.', C.', p).'
+ L = place (sys.', p).'   
+ @deftypefn {Function File} rlocus (@var{sys}) 
+ @deftypefnx {Function File} {[@var{rldata}, @var{k}] =} rlocus (@var{sys}[, @var{increment}, @var{min_k}, @var{max_k}]) 
+ Display root locus plot of the specified @acronym{SISO} system.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.  Must be a single-input and single-output (SISO) system.
+ @item min_k
+ Minimum value of @var{k}.
+ @item max_k
+ Maximum value of @var{k}.
+ @item increment
+ The increment used in computing gain values.
+ @end table
+
+ @strong{Outputs}
+ @table @var 
+ @item rldata
+ Data points plotted: in column 1 real values, in column 2 the imaginary values.
+ @item k
+ Gains for real axis break points.
+ @end table
+
+ @strong{Block Diagram}
+ @example
+ @group
+  u    +         +---+      +------+             y
+ ------>(+)----->| k |----->| SISO |-------+------->
+         ^ -     +---+      +------+       |
+         |                                 |
+         +---------------------------------+
+ @end group
+ @end example
+ @end deftypefn
+@section Linear-Quadratic Control
+
+ @deftypefn {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{sys}, @var{q}, @var{r})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{sys}, @var{q}, @var{r}, @var{s})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e})
+ Linear-quadratic regulator for discrete-time systems.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ Continuous or discrete-time LTI model.
+ @item a
+ State transition matrix of discrete-time system.
+ @item b
+ Input matrix of discrete-time system.
+ @item q
+ State weighting matrix.
+ @item r
+ Input weighting matrix.
+ @item s
+ Optional cross term matrix.  If @var{s} is not specified, a zero matrix is assumed.
+ @item e
+ Optional descriptor matrix.  If @var{e} is not specified, an identity matrix is assumed.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item g
+ State feedback matrix.
+ @item x
+ Unique stabilizing solution of the discrete-time Riccati equation.
+ @item l
+ Closed-loop poles.
+ @end table
+
+ @strong{Equations}
+ @example
+ @group
+ x[k+1] = A x[k] + B u[k],   x[0] = x0
+
+         inf
+ J(x0) = SUM (x' Q x  +  u' R u  +  2 x' S u)
+         k=0
+
+ L = eig (A - B*G)
+ @end group
+ @end example
+ @seealso{dare, care, lqr}
+ @end deftypefn
+
+ @deftypefn {Function File} {@var{est} =} estim (@var{sys}, @var{l})
+ @deftypefnx {Function File} {@var{est} =} estim (@var{sys}, @var{l}, @var{sensors}, @var{known})
+ Return state estimator for a given estimator gain.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ LTI model.
+ @item l
+ State feedback matrix.
+ @item sensors
+ Indices of measured output signals y from @var{sys}.  If omitted, all outputs are measured.
+ @item known
+ Indices of known input signals u (deterministic) to @var{sys}.  All other inputs to @var{sys}
+ are assumed stochastic.  If argument @var{known} is omitted, no inputs u are known.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item est
+ State-space model of estimator.
+ @end table
+ @seealso{kalman, place}
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{est}, @var{g}, @var{x}] =} kalman (@var{sys}, @var{q}, @var{r})
+ @deftypefnx {Function File} {[@var{est}, @var{g}, @var{x}] =} kalman (@var{sys}, @var{q}, @var{r}, @var{s})
+ @deftypefnx {Function File} {[@var{est}, @var{g}, @var{x}] =} kalman (@var{sys}, @var{q}, @var{r}, @var{[]}, @var{sensors}, @var{known})
+ @deftypefnx {Function File} {[@var{est}, @var{g}, @var{x}] =} kalman (@var{sys}, @var{q}, @var{r}, @var{s}, @var{sensors}, @var{known})
+ Design Kalman estimator for LTI systems.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ Nominal plant model.
+ @item q
+ Covariance of white process noise.
+ @item r
+ Covariance of white measurement noise.
+ @item s
+ Optional cross term covariance.  Default value is 0.
+ @item sensors
+ Indices of measured output signals y from @var{sys}.  If omitted, all outputs are measured.
+ @item known
+ Indices of known input signals u (deterministic) to @var{sys}.  All other inputs to @var{sys}
+ are assumed stochastic.  If argument @var{known} is omitted, no inputs u are known.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item est
+ State-space model of the Kalman estimator.
+ @item g
+ Estimator gain.
+ @item x
+ Solution of the Riccati equation.
+ @end table
+
+ @strong{Block Diagram}
+ @example
+ @group
+                                  u  +-------+         ^
+       +---------------------------->|       |-------> y
+       |    +-------+     +       y  |  est  |         ^
+ u ----+--->|       |----->(+)------>|       |-------> x
+            |  sys  |       ^ +      +-------+
+ w -------->|       |       |
+            +-------+       | v
+
+ Q = cov (w, w')     R = cov (v, v')     S = cov (w, v')
+ @end group
+ @end example
+
+ @seealso{care, dare, estim, lqr}
+ @end deftypefn
+
+ @deftypefn {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{sys}, @var{q}, @var{r})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{sys}, @var{q}, @var{r}, @var{s})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e})
+ @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} lqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e})
+ Linear-quadratic regulator.
+
+ @strong{Inputs}
+ @table @var
+ @item sys
+ Continuous or discrete-time LTI model.
+ @item a
+ State transition matrix of continuous-time system.
+ @item b
+ Input matrix of continuous-time system.
+ @item q
+ State weighting matrix.
+ @item r
+ Input weighting matrix.
+ @item s
+ Optional cross term matrix.  If @var{s} is not specified, a zero matrix is assumed.
+ @item e
+ Optional descriptor matrix.  If @var{e} is not specified, an identity matrix is assumed.
+ @end table
+
+ @strong{Outputs}
+ @table @var
+ @item g
+ State feedback matrix.
+ @item x
+ Unique stabilizing solution of the continuous-time Riccati equation.
+ @item l
+ Closed-loop poles.
+ @end table
+
+ @strong{Equations}
+ @example
+ @group
+ .
+ x = A x + B u,   x(0) = x0
+
+         inf
+ J(x0) = INT (x' Q x  +  u' R u  +  2 x' S u)  dt
+          0
+
+ L = eig (A - B*G)
+ @end group
+ @end example
+ @seealso{care, dare, dlqr}
+ @end deftypefn
+@section Robust Control
+
+ @deftypefn{Function File} {@var{P} =} augw (@var{G}, @var{W1}, @var{W2}, @var{W3})
+ Extend plant for stacked S/KS/T problem.  Subsequently, the robust control problem
+ can be solved by h2syn or hinfsyn.
+
+ @strong{Inputs}
+ @table @var
+ @item G
+ LTI model of plant.
+ @item W1
+ LTI model of performance weight.  Bounds the largest singular values of sensitivity @var{S}.
+ Model must be empty @code{[]}, SISO or of appropriate size.
+ @item W2
+ LTI model to penalize large control inputs.  Bounds the largest singular values of @var{KS}.
+ Model must be empty @code{[]}, SISO or of appropriate size.
+ @item W3
+ LTI model of robustness and noise sensitivity weight.  Bounds the largest singular values of 
+ complementary sensitivity @var{T}.  Model must be empty @code{[]}, SISO or of appropriate size.
+ @end table
+
+ All inputs must be proper/realizable.
+ Scalars, vectors and matrices are possible instead of LTI models.
+
+ @strong{Outputs}
+ @table @var
+ @item P
+ State-space model of augmented plant.
+ @end table
+
+ @strong{Block Diagram}
+ @example
+ @group
+
+     | W1 | -W1*G |     z1 = W1 r  -  W1 G u
+     | 0  |  W2   |     z2 =          W2   u
+ P = | 0  |  W3*G |     z3 =          W3 G u
+     |----+-------|
+     | I  |    -G |     e  =    r  -     G u
+                                                       +------+  z1
+             +---------------------------------------->|  W1  |----->
+             |                                         +------+
+             |                                         +------+  z2
+             |                 +---------------------->|  W2  |----->
+             |                 |                       +------+
+  r   +    e |   +--------+  u |   +--------+  y       +------+  z3
+ ----->(+)---+-->|  K(s)  |----+-->|  G(s)  |----+---->|  W3  |----->
+        ^ -      +--------+        +--------+    |     +------+
+        |                                        |
+        +----------------------------------------+
+
+                +--------+
+                |        |-----> z1 (p1x1)          z1 = W1 e
+  r (px1) ----->|  P(s)  |-----> z2 (p2x1)          z2 = W2 u
+                |        |-----> z3 (p3x1)          z3...
 
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