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## Copyright (C) 1996 John W. Eaton
##
## This file is part of Octave.
##
## Octave 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 2, or (at your option)
## any later version.
##
## Octave 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 Octave; see the file COPYING. If not, write to the Free
## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
## Usage: [Ad, Bd] = c2d (Ac, Bc, T)
##
## converts the continuous time system described by:
## .
## x = Ac x + Bc u
##
## into a discrete time equivalent model via the matrix exponential
##
## x[n+1] = Ad x[n] + Bd u[n]
##
## assuming a zero-order hold on the input and sample time T.
## Author: R.B. Tenison <btenison@eng.auburn.edu>
## Created: October 1993
## Adapted-By: jwe
function [Ad, Bd] = c2d (Ac, Bc, T)
## check args
if (nargin != 3)
usage ("c2d (Ac, Bc, T)");
endif
[ma, na] = size (Ac);
[mb, nb] = size (Bc);
if (ma != na)
error ("c2d: Ac must be square");
endif
if (ma != mb)
error ("c2d: Ac and Bc must have the same number of rows");
endif
matexp = expm ([[Ac, Bc] * T; (zeros (nb, na+nb))]);
Ad = matexp (1:na, 1:na);
Bd = matexp (1:na, na+1:na+nb);
endfunction
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