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## Copyright (C) 1996, 2000, 2002, 2004, 2005, 2006, 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{y}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})
## Produce output for a linear simulation of a system; produces
## a plot for the output of the system, @var{sys}.
##
## @var{u} is an array that contains the system's inputs. Each row in @var{u}
## corresponds to a different time step. Each column in @var{u} corresponds to a
## different input. @var{t} is an array that contains the time index of the
## system; @var{t} should be regularly spaced. If initial conditions are required
## on the system, the @var{x0} vector should be added to the argument list.
##
## When the lsim function is invoked a plot is not displayed;
## however, the data is returned in @var{y} (system output)
## and @var{x} (system states).
## @end deftypefn
## Author: David Clem
## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: July 1995
## modified by John Ingram for system format August 1996
function [y, x] = lsim (sys, u, t, x0)
if (nargin < 3 || nargin > 4)
print_usage ();
endif
if (! isstruct (sys))
error ("sys must be in system data structure");
endif
sys = sysupdate (sys,"ss");
[ncstates, ndstates, nin, nout] = sysdimensions (sys);
[a, b, c, d] = sys2ss (sys);
if (nargin == 3)
x0 = zeros (columns (a), 1);
endif
if (rows (u) != length (t))
error ("lsim: There should be an input value (row) for each time instant");
endif
if (columns (u) != columns (d))
error ("lsim: U and d should have the same number of inputs");
endif
if (columns (x0) > 1)
error ("lsim: Initial condition vector should have only one column");
endif
if (rows (x0) > rows (a))
error ("lsim: Initial condition vector is too large");
endif
Ts = 0;
t(2)-t(1);
u=u';
n = max (size (t));
if (isa (t, "single"))
tol = 10 * eps ("single");
else
tol = 10 * eps;
endif
for ii = 1:(n-1)
## check if step size changed
## FIXME -- this is probably not the best test, but it is
## better than a test for exact equality.
if (abs (t(ii+1) - t(ii) - Ts) > tol)
Ts = t(ii+1) - t(ii);
## [F,G] = c2d(a,b,Ts);
dsys = c2d (sys, Ts);
[F, G] = sys2ss (dsys);
endif
x(:,ii) = x0;
x0 = F*x0 + G*u(:,ii);
endfor
## pick up last point
x(:,n) = x0;
y = c*x + d*u;
if (nargout == 0)
plot (t, y);
y = [];
x = [];
endif
endfunction
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