X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2Fgram.m;fp=octave_packages%2Fcontrol-2.3.52%2Fgram.m;h=45f59bd4a5a570d25a87004033a3d452ff9b2735;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05

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+## Copyright (C) 1996, 2000, 2003, 2004, 2005, 2007
+##               Auburn University. All rights reserved.
+##
+##
+## 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 3 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 this program; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @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
+
+## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
+
+## Adapted-By: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Date: October 2009
+## Version: 0.2
+
+function W = gram (argin1, argin2)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (ischar (argin2))     # the function was called as "gram (sys, mode)"
+    sys = argin1;
+
+    if (! isa (sys, "lti"))
+      error ("gram: first argument must be an LTI model");
+    endif
+
+    [a, b, c] = ssdata (sys);
+
+    if (strncmpi (argin2, "o", 1))
+      a = a.';
+      b = c.';
+    elseif (! strncmpi (argin2, "c", 1))
+      print_usage ();
+    endif
+  else                     # the function was called as "gram (a, b)"
+    a = argin1;
+    b = argin2;
+
+    ## assume that a and b are matrices of continuous-time system
+    ## values of b, c and d are irrelevant for system stability
+    sys = ss (a, b, zeros (1, columns (a)), zeros (1, columns (b)));
+  endif
+
+  if (! isstable (sys))
+    error ("gram: system matrix a must be stable");
+  endif
+
+  if (isct (sys))
+    W = lyap (a, b*b.');   # let lyap do the error checking about dimensions
+  else  # discrete-time system
+    W = dlyap (a, b*b.');  # let dlyap do the error checking about dimensions
+  endif
+
+endfunction
+
+
+%!test
+%! a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
+%! b = [1 0; 0 -1; 0 1];
+%! c = [0 0 1; 1 1 0]; ## it doesn't matter what the value of c is
+%! Wc = gram (ss (a, b, c), "c");
+%! assert (a * Wc + Wc * a.' + b * b.', zeros (size (a)))
+
+%!test
+%! a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
+%! b = [1 0; 0 -1; 0 1]; ## it doesn't matter what the value of b is
+%! c = [0 0 1; 1 1 0];
+%! Wo = gram (ss (a, b, c), "o");
+%! assert (a.' * Wo + Wo * a + c.' * c, zeros (size (a)))
+
+%!test
+%! a = [-1 0 0; 1/2 -1 0; 1/2 0 -1];
+%! b = [1 0; 0 -1; 0 1];
+%! Wc = gram (a, b);
+%! assert (a * Wc + Wc * a.' + b * b.', zeros (size (a)))
+
+%!test
+%! a = [-1 0 0; 1/2 1 0; 1/2 0 -1] / 2;
+%! b = [1 0; 0 -1; 0 1];
+%! c = [0 0 1; 1 1 0]; ## it doesn't matter what the value of c is
+%! d = zeros (rows (c), columns (b)); ## it doesn't matter what the value of d is
+%! Ts = 0.1; ## Ts != 0
+%! Wc = gram (ss (a, b, c, d, Ts), "c");
+%! assert (a * Wc * a.' - Wc + b * b.', zeros (size (a)), 1e-12)
+
+%!test
+%! a = [-1 0 0; 1/2 1 0; 1/2 0 -1] / 2;
+%! b = [1 0; 0 -1; 0 1]; ## it doesn't matter what the value of b is
+%! c = [0 0 1; 1 1 0];
+%! d = zeros (rows (c), columns (b)); ## it doesn't matter what the value of d is
+%! Ts = 0.1; ## Ts != 0
+%! Wo = gram (ss (a, b, c, d, Ts), "o");
+%! assert (a.' * Wo * a - Wo + c.' * c, zeros (size (a)), 1e-12)
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