This is are.m in view mode; [Download] [Up]
## 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: x = are (a, b, c {,opt})
##
## Solves algebraic riccati equation
##
## a' x + x a - x b x + c = 0
##
## for identically dimensioned square matrices a, b, c. If b (c) is not
## square, then the function attempts to use b * b' (c' * c) instead.
##
## Solution method: apply Laub's Schur method (IEEE Trans. Auto. Contr,
## 1979) to the appropriate Hamiltonian matrix.
##
## opt is an option passed to the eigenvalue balancing routine default is "B".
##
## See also: balance
## Author: A. S. Hodel <scotte@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe
function x = are (a, b, c, opt)
if (nargin == 3 || nargin == 4)
if (nargin == 4)
if (! (strcmp (opt, "N") || strcmp (opt, "P") ...
|| strcmp (opt, "S") || strcmp (opt, "B") ...
|| strcmp (opt, "n") || strcmp (opt, "p") ...
|| strcmp (opt, "s") || strcmp (opt, "b")))
warning ("are: opt has an invalid value; setting to B");
opt = "B";
endif
else
opt = "B";
endif
if ((n = is_square(a)) == 0)
error ("are: a is not square");
endif
if (is_controllable(a,b) == 0)
warning ("are: a, b are not controllable");
endif
if ((m = is_square (b)) == 0)
b = b * b';
m = rows (b);
endif
if (is_observable (a, c) == 0)
warning ("are: a,c are not observable");
endif
if ((p = is_square (c)) == 0)
c = c' * c;
p = rows (c);
endif
if (n != m || n != p)
error ("are: a, b, c not conformably dimensioned.");
endif
## Should check for controllability/observability here
## use Boley-Golub (Syst. Contr. Letters, 1984) method, not the
##
## n-1
## rank ([ B A*B ... A^ *B]) method
[d, h] = balance ([a, -b; -c, -a'], opt);
[u, s] = schur (h, "A");
u = d * u;
n1 = n + 1;
n2 = 2 * n;
x = u (n1:n2, 1:n) / u (1:n, 1:n);
else
usage ("x = are (a, b, c)");
endif
endfunction
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.