## Copyright (C) 1996 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 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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} dgram (@var{a}, @var{b})
## Return controllability gramian of discrete time system
## @iftex
## @tex
## $$ x_{k+1} = ax_k + bu_k $$
## @end tex
## @end iftex
## @ifinfo
## @example
##   x(k+1) = a x(k) + b u(k)
## @end example
## @end ifinfo
## 
## @strong{Inputs}
## @table @var
## @item a
## @var{n} by @var{n} matrix
## @item b
## @var{n} by @var{m} matrix
## @end table
##
## @strong{Output}
## @table @var
## @item m 
## @var{n} by @var{n} matrix, satisfies
## @iftex
## @tex
## $$ ama^T - m + bb^T = 0 $$
## @end tex
## @end iftex
## @ifinfo
## @var{m} (@var{n} by @var{n}) satisfies
## @example
##  a m a' - m + b*b' = 0
## @end example
## @end ifinfo
## @end table
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: July 1995

function m = dgram (a, b)

  ## let dlyap do the error checking...

  m = dlyap (a, b*b');

endfunction