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[Octave-cvsupdate] SF.net SVN: octave:[7283] trunk/octave-forge/main/control/inst
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From: <par...@us...> - 2010-05-02 17:47:49
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Revision: 7283
http://octave.svn.sourceforge.net/octave/?rev=7283&view=rev
Author: paramaniac
Date: 2010-05-02 17:47:43 +0000 (Sun, 02 May 2010)
Log Message:
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control: add ctrbf.m and obsvf.m (thanks to Benjamin Fernandez)
Added Paths:
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trunk/octave-forge/main/control/inst/ctrbf.m
trunk/octave-forge/main/control/inst/obsvf.m
Added: trunk/octave-forge/main/control/inst/ctrbf.m
===================================================================
--- trunk/octave-forge/main/control/inst/ctrbf.m (rev 0)
+++ trunk/octave-forge/main/control/inst/ctrbf.m 2010-05-02 17:47:43 UTC (rev 7283)
@@ -0,0 +1,76 @@
+## Copyright (C) 2010 Benjamin Fernandez <ma...@be...>
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING. If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {[@var{Abar}, @var{Bbar}, @var{Cbar}, @var{T}, @var{K}] =} ctrbf (@var{A}, @var{B}, @var{C})
+## @deftypefnx{Function File} {[@var{Abar}, @var{Bbar}, @var{Cbar}, @var{T}, @var{K}] =} ctrbf (@var{A}, @var{B}, @var{C}, @var{TOL})
+## If Co=ctrb(A,B) has rank r <= n = SIZE(A,1), then there is a
+## similarity transformation Tc such that Tc = [t1 t2] where t1
+## is the controlable subspace and t2 is orthogonal to t1
+##
+## @example
+## @group
+## Abar = Tc \ A * Tc , Bbar = Tc \ B , Cbar = C * Tc
+## @end group
+## @end example
+##
+## and the transformed system has the form
+##
+## @example
+## @group
+## | Ac A12| | Bc |
+## Abar = |----------|, Bbar = | ---|, Cbar = [Cc | Cnc].
+## | 0 Anc| | 0 |
+## @end group
+## @end example
+##
+## where (Ac,Bc) is controllable, and Cc(sI-Ac)^(-1)Bc = C(sI-A)^(-1)B.
+## and the system is stabilizable if Anc has no eigenvalues in
+## the right half plane. The last output K is a vector of length n
+## containing the number of controllable states.
+## @end deftypefn
+
+## Author: Benjamin Fernandez <benjas@benjas-laptop>
+## Created: 2010-04-30
+
+function [Abar, Bbar, Cbar, T, K] = ctrbf (A, B, C, TOL)
+
+ if (nargin<3 || nargin>4)
+ print_usage ();
+ end
+
+ n = length (A);
+
+ if (nargin==3)
+ TOL = n*norm (A,1)*eps;
+ end
+
+ Co = ctrb (A, B);
+ [nrc, ncc] = size (Co);
+ rco = rank (Co,TOL);
+ lr = nrc-rco;
+ [U, S, V] = svd (Co);
+ K = U(:, 1:rco); # Basis column space
+ T = U; # [B orth(B)]
+ Abar = T\A*T;
+ Bbar = T\B;
+ Cbar = C*T;
+ Anc = Abar(n-(n-rco)+1:n, n-(n-rco)+1:n);
+ Ac = Abar(1:rco, 1:rco);
+ Bc = Bbar(1:rco, :);
+ Cc = Cbar(:, 1:rco);
+
+endfunction
\ No newline at end of file
Added: trunk/octave-forge/main/control/inst/obsvf.m
===================================================================
--- trunk/octave-forge/main/control/inst/obsvf.m (rev 0)
+++ trunk/octave-forge/main/control/inst/obsvf.m 2010-05-02 17:47:43 UTC (rev 7283)
@@ -0,0 +1,76 @@
+## Copyright (C) 2010 Benjamin Fernandez
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING. If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {[@var{Abar}, @var{Bbar}, @var{Cbar}, @var{T}, @var{K}] =} obsvf (@var{A}, @var{B}, @var{C})
+## @deftypefnx{Function File} {[@var{Abar}, @var{Bbar}, @var{Cbar}, @var{T}, @var{K}] =} obsvf (@var{A}, @var{B}, @var{C}, @var{TOL})
+## If Ob=obsv(A,C) has rank r <= n = SIZE(A,1), then there is a
+## similarity transformation Tc such that To = [t1;t2] where t1 is c
+## and t2 is orthogonal to t1
+##
+## @example
+## @group
+## Abar = To \ A * To , Bbar = To \ B , Cbar = C * To
+## @end group
+## @end example
+##
+## and the transformed system has the form
+##
+## @example
+## @group
+## | Ao 0 | | Bo |
+## Abar = |----------|, Bbar = | --- |, Cbar = [Co | 0 ].
+## | A21 Ano| | Bno |
+## @end group
+## @end example
+##
+## where (Ao,Bo) is observable, and Co(sI-Ao)^(-1)Bo = C(sI-A)^(-1)B. And
+## system is detectable if Ano has no eigenvalues in the right
+## half plane. The last output K is a vector of length n containing the
+## number of observable states.
+## @end deftypefn
+
+## Author: Benjamin Fernandez <benjas@benjas-laptop>
+## Created: 2010-05-02
+
+function [Abar, Bbar, Cbar, T, K] = obsvf (A, B, C, TOL)
+
+ if (nargin<3 || nargin>4)
+ print_usage ();
+ end
+
+ n = length (A);
+
+ if (nargin==3)
+ TOL = n*norm (A, 1)*eps;
+ end
+
+ Ob = obsv (A, C);
+ [nro, nco] = size (Ob);
+ rob = rank (Ob);
+ lr = nco-rob;
+ [U, S, V] = svd (Ob);
+ K = V(:, 1:rob); # Basis raw space
+ T = V; # [c;orth(c)];
+ Abar = T\A*T;
+ Bbar = T\B;
+ Cbar = C*T;
+ Ano = Abar(n-(n-rob)+1:n, n-(n-rob)+1:n)
+ Ao = Abar(1:rob, 1:rob);
+ Bo = Bbar(1:rob, :);
+ Co = Cbar(:, 1:rob);
+
+endfunction
\ No newline at end of file
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