Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / obsvf.m

diff --git a/octave_packages/control-2.3.52/obsvf.m b/octave_packages/control-2.3.52/obsvf.m
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+## Copyright (C) 2010   Benjamin Fernandez 
+## Copyright (C) 2011   Lukas F. Reichlin
+## 
+## This file is part of LTI Syncope.
+##
+## LTI Syncope 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 3 of the License, or
+## (at your option) any later version.
+##
+## LTI Syncope 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 LTI Syncope.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {[@var{sysbar}, @var{T}, @var{K}] =} obsvf (@var{sys})
+## @deftypefnx{Function File} {[@var{sysbar}, @var{T}, @var{K}] =} obsvf (@var{sys}, @var{tol})
+## @deftypefnx{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
+## Version: 0.1
+
+function [ac, bc, cc, z, ncont] = obsvf (a, b = [], c, tol = [])
+
+  if (nargin < 1 || nargin > 4)
+    print_usage ();
+  endif
+  
+  if (isa (a, "lti"))
+    if (nargin > 2)
+      print_usage ();
+    endif
+    [ac, bc, cc] = ctrbf (a.', b);      # [sysbar, z, ncont] = ctrbf (sys.', tol);
+    ac = ac.';
+    z = ncont = [];
+  else
+    if (nargin < 3)
+      print_usage ();
+    endif
+    [ac, tmp, cc, z, ncont] = ctrbf (a.', c.', b.', tol);
+    ac = ac.';
+    bc = cc.';
+    cc = tmp.';
+  endif
+
+endfunction