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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: is_controllable (a, b {,tol})
##
## Returns 1 if the pair (a, b) is controllable, or 0 if not.
##
## See also: size, rows, columns, length, is_matrix, is_scalar, is_vector
##
## This should really use the method below, but I'm being lazy for now:
##
## Controllability is determined by applying Arnoldi iteration with
## complete re-orthogonalization to obtain an orthogonal basis of the
## Krylov subspace.
##
## (FIX ME... The Krylov subspace approach is not done yet!)
## n-1
## span ([b,a*b,...,a^ b]).
##
## tol is a roundoff paramter, set to 2*eps if omitted.
## Author: A. S. Hodel <scotte@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe
function retval = is_controllable (a, b, tol)
if (nargin == 2 || nargin == 3)
n = is_square (a);
[nr, nc] = size (b);
if (n == 0 || n != nr || nc == 0)
retval = 0;
else
m = b;
tmp = b;
for ii = 1:(n-1)
tmp = a * tmp;
m = [m, tmp];
endfor
## If n is of any significant size, m will be low rank, so be careful!
if (nargin == 3)
if (is_scalar (tol))
retval = (rank (m, tol) == n);
else
error ("is_controllable: tol must be a scalar");
endif
else
retval = (rank (m) == n);
endif
endif
else
usage ("is_controllable (a, b)");
endif
endfunction
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