--- /dev/null
+## Copyright (C) 2010 Lukas F. Reichlin
+##
+## This file is part of LTI Syncope.
+##
+## LTI Syncope 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.
+##
+## LTI Syncope 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 LTI Syncope. If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {@var{x} =} dlyap (@var{a}, @var{b})
+## @deftypefnx{Function File} {@var{x} =} dlyap (@var{a}, @var{b}, @var{c})
+## @deftypefnx{Function File} {@var{x} =} dlyap (@var{a}, @var{b}, @var{[]}, @var{e})
+## Solve discrete-time Lyapunov or Sylvester equations.
+##
+## @strong{Equations}
+## @example
+## @group
+## AXA' - X + B = 0 (Lyapunov Equation)
+##
+## AXB' - X + C = 0 (Sylvester Equation)
+##
+## AXA' - EXE' + B = 0 (Generalized Lyapunov Equation)
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB03MD, SB04QD and SG03AD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{dlyapchol, lyap, lyapchol}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: January 2010
+## Version: 0.2.1
+
+function [x, scale] = dlyap (a, b, c, e)
+
+ scale = 1;
+
+ switch (nargin)
+ case 2 # Lyapunov equation
+
+ if (! is_real_square_matrix (a, b))
+ ## error ("dlyap: a, b must be real and square");
+ error ("dlyap: %s, %s must be real and square", \
+ inputname (1), inputname (2));
+ endif
+
+ if (rows (a) != rows (b))
+ ## error ("dlyap: a, b must have the same number of rows");
+ error ("dlyap: %s, %s must have the same number of rows", \
+ inputname (1), inputname (2));
+ endif
+
+ [x, scale] = slsb03md (a, -b, true); # AXA' - X = -B
+
+ ## x /= scale; # 0 < scale <= 1
+
+ case 3 # Sylvester equation
+
+ if (! is_real_square_matrix (a, b))
+ ## error ("dlyap: a, b must be real and square");
+ error ("dlyap: %s, %s must be real and square", \
+ inputname (1), inputname (2));
+ endif
+
+ if (! is_real_matrix (c) || rows (c) != rows (a) || columns (c) != columns (b))
+ ## error ("dlyap: c must be a real (%dx%d) matrix", rows (a), columns (b));
+ error ("dlyap: %s must be a real (%dx%d) matrix", \
+ rows (a), columns (b), inputname (3));
+ endif
+
+ x = slsb04qd (-a, b, c); # AXB' - X = -C
+
+ case 4 # generalized Lyapunov equation
+
+ if (! isempty (c))
+ print_usage ();
+ endif
+
+ if (! is_real_square_matrix (a, b, e))
+ ## error ("dlyap: a, b, e must be real and square");
+ error ("dlyap: %s, %s, %s must be real and square", \
+ inputname (1), inputname (2), inputname (4));
+ endif
+
+ if (rows (b) != rows (a) || rows (e) != rows (a))
+ ## error ("dlyap: a, b, e must have the same number of rows");
+ error ("dlyap: %s, %s, %s must have the same number of rows", \
+ inputname (1), inputname (2), inputname (4));
+ endif
+
+ if (! issymmetric (b))
+ ## error ("dlyap: b must be symmetric");
+ error ("dlyap: %s must be symmetric", \
+ inputname (2));
+ endif
+
+ [x, scale] = slsg03ad (a, e, -b, true); # AXA' - EXE' = -B
+
+ ## x /= scale; # 0 < scale <= 1
+
+ otherwise
+ print_usage ();
+
+ endswitch
+
+ if (scale < 1)
+ warning ("dlyap: solution scaled by %g to prevent overflow", scale);
+ endif
+
+endfunction
+
+
+## Lyapunov
+%!shared X, X_exp
+%! A = [3.0 1.0 1.0
+%! 1.0 3.0 0.0
+%! 0.0 0.0 3.0];
+%!
+%! B = [25.0 24.0 15.0
+%! 24.0 32.0 8.0
+%! 15.0 8.0 40.0];
+%!
+%! X = dlyap (A.', -B);
+%!
+%! X_exp = [2.0000 1.0000 1.0000
+%! 1.0000 3.0000 0.0000
+%! 1.0000 0.0000 4.0000];
+%!
+%!assert (X, X_exp, 1e-4);
+
+## Sylvester
+%!shared X, X_exp
+%! A = [1.0 2.0 3.0
+%! 6.0 7.0 8.0
+%! 9.0 2.0 3.0];
+%!
+%! B = [7.0 2.0 3.0
+%! 2.0 1.0 2.0
+%! 3.0 4.0 1.0];
+%!
+%! C = [271.0 135.0 147.0
+%! 923.0 494.0 482.0
+%! 578.0 383.0 287.0];
+%!
+%! X = dlyap (-A, B, C);
+%!
+%! X_exp = [2.0000 3.0000 6.0000
+%! 4.0000 7.0000 1.0000
+%! 5.0000 3.0000 2.0000];
+%!
+%!assert (X, X_exp, 1e-4);
+
+## Generalized Lyapunov
+## TODO: add a test
\ No newline at end of file