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## Copyright (C) 1997, 2000, 2002, 2004, 2005, 2006, 2007 Kai P. Mueller
##
##
## 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} {} obsv (@var{sys}, @var{c})
## @deftypefnx {Function File} {} obsv (@var{a}, @var{c})
## Build observability matrix:
## @iftex
## @tex
## $$ Q_b = \left[ \matrix{ C \cr
## CA \cr
## CA^2 \cr
## \vdots \cr
## CA^{n-1} } \right ] $$
## @end tex
## @end iftex
## @ifinfo
## @example
## @group
## | C |
## | CA |
## Qb = | CA^2 |
## | ... |
## | CA^(n-1) |
## @end group
## @end example
## @end ifinfo
## of a system data structure or the pair (@var{a}, @var{c}).
##
## The numerical properties of @command{is_observable}
## are much better for observability tests.
## @end deftypefn
## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
## Created: November 4, 1997
function Qb = obsv (sys, c)
if (nargin == 2)
a = sys;
elseif (nargin == 1 && isstruct(sys))
sysupdate (sys, "ss");
[a, b, c] = sys2ss (sys);
else
print_usage ();
endif
if (! is_abcd (a, c'))
Qb = [];
else
## no need to check dimensions, we trust is_abcd().
[na, ma] = size (a);
[nc, mc] = size (c);
Qb = zeros (na*nc, ma);
for i = 1:na
Qb((i-1)*nc+1:i*nc, :) = c;
c = c * a;
endfor
endif
endfunction
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