## Copyright (C) 1993, 1994, 1995 Auburn University.  All rights reserved.
##
## 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 3 of the License, 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, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} is_stable (@var{a}, @var{tol}, @var{dflg})
## @deftypefnx {Function File} {} is_stable (@var{sys}, @var{tol})
## Returns 1 if the matrix @var{a} or the system @var{sys}
## is stable, or 0 if not.
##
## @strong{Inputs}
## @table @var
## @item  tol
## is a roundoff parameter, set to 200*@code{eps} if omitted.
## @item dflg
## Digital system flag (not required for system data structure):
## @table @code
## @item @var{dflg} != 0
## stable if eig(a) is in the unit circle
##
## @item @var{dflg} == 0
## stable if eig(a) is in the open LHP (default)
## @end table
## @end table
## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector
## is_observable, is_stabilizable, is_detectable, krylov, krylovb}
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: August 1993
## Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for systems
## Updated to simpler form by a.s.hodel 1998

function retval = is_stable (a, tol, disc)

  if( (nargin < 1) | (nargin > 3) )   print_usage ();
  elseif(isstruct(a))
    ## system was passed
    if(nargin < 3)                      disc = is_digital(a);
    elseif(disc != is_digital(a))
      warning("is_stable: disc =%d does not match system",disc)
    endif
    sys = sysupdate(a,"ss");
    a = sys2ss(sys);
  else
    if(nargin < 3)              disc = 0;               endif
    if(issquare(a) == 0)
      error("A(%dx%d) must be square",rows(A), columns(A));
    endif
  endif

  if(nargin < 2)                tol = 200*eps;
  elseif( !isscalar(tol) )
    error("is_stable: tol(%dx%d) must be a scalar",rows(tol),columns(tol));
  endif

  l = eig(a);
  if(disc)      nbad = sum(abs(l)*(1+tol) > 1);
  else          nbad = sum(real(l)+tol > 0);            endif
  retval = (nbad == 0);

endfunction
