Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/control-2.3.52/covar.m b/octave_packages/control-2.3.52/covar.m
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+## Copyright (C) 2010   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{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 Gaussian 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
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: January 2010
+## Version: 0.1
+
+function [p, q] = covar (sys, w)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+  
+  if (! isa (sys, "lti"))
+    error ("covar: first argument must be an LTI model");
+  endif
+  
+  if (! isstable (sys))
+    error ("covar: system must be stable");
+  endif
+  
+  [a, b, c, d] = ssdata (sys);
+  
+  if (isct (sys))
+    if (any (d(:)))
+      error ("covar: system is not strictly proper");
+    endif
+    
+    q = lyap (a, b*w*b.');
+    p = c*q*c.';
+  else
+    q = dlyap (a, b*w*b.');
+    p = c*q*c.' + d*w*d.';
+  endif
+
+endfunction
+
+## continuous-time
+%!shared p, q, p_exp, q_exp
+%! sys = ss (-1, 1, 1, 0);
+%! [p, q] = covar (sys, 5);
+%! p_exp = 2.5000;
+%! q_exp = 2.5000;
+%!assert (p, p_exp, 1e-4);
+%!assert (q, q_exp, 1e-4);
+
+## discrete-time
+%!shared p, q, p_exp, q_exp
+%! sys = ss ([-0.2, -0.5; 1, 0], [2; 0], [1, 0.5], [0], 0.1);
+%! [p, q] = covar (sys, 5);
+%! p_exp = 30.3167;
+%! q_exp = [27.1493, -3.6199; -3.6199, 27.1493];
+%!assert (p, p_exp, 1e-4);
+%!assert (q, q_exp, 1e-4);
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