X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fcontrol-2.3.52%2Flyap.m;fp=octave_packages%2Fcontrol-2.3.52%2Flyap.m;h=9052a5b80b6c3456f2f54f28cbc499d69d730a96;hp=0000000000000000000000000000000000000000;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hpb=1705066eceaaea976f010f669ce8e972f3734b05
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+## 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 .
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {@var{x} =} lyap (@var{a}, @var{b})
+## @deftypefnx{Function File} {@var{x} =} lyap (@var{a}, @var{b}, @var{c})
+## @deftypefnx{Function File} {@var{x} =} lyap (@var{a}, @var{b}, @var{[]}, @var{e})
+## Solve continuous-time Lyapunov or Sylvester equations.
+##
+## @strong{Equations}
+## @example
+## @group
+## AX + XA' + B = 0 (Lyapunov Equation)
+##
+## AX + XB + C = 0 (Sylvester Equation)
+##
+## AXE' + EXA' + B = 0 (Generalized Lyapunov Equation)
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB03MD, SB04MD and SG03AD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{lyapchol, dlyap, dlyapchol}
+## @end deftypefn
+
+## Author: Lukas Reichlin
+## Created: January 2010
+## Version: 0.2.1
+
+function [x, scale] = lyap (a, b, c, e)
+
+ scale = 1;
+
+ switch (nargin)
+ case 2 # Lyapunov equation
+
+ if (! is_real_square_matrix (a, b))
+ ## error ("lyap: a, b must be real and square");
+ error ("lyap: %s, %s must be real and square", \
+ inputname (1), inputname (2));
+ endif
+
+ if (rows (a) != rows (b))
+ ## error ("lyap: a, b must have the same number of rows");
+ error ("lyap: %s, %s must have the same number of rows", \
+ inputname (1), inputname (2));
+
+ endif
+
+ [x, scale] = slsb03md (a, -b, false); # AX + XA' = -B
+
+ ## x /= scale; # 0 < scale <= 1
+
+ case 3 # Sylvester equation
+
+ if (! is_real_square_matrix (a, b))
+ ## error ("lyap: a, b must be real and square");
+ error ("lyap: %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 ("lyap: c must be a real (%dx%d) matrix", rows (a), columns (b));
+ error ("lyap: %s must be a real (%dx%d) matrix", \
+ rows (a), columns (b), inputname (3));
+ endif
+
+ x = slsb04md (a, b, -c); # AX + XB = -C
+
+ case 4 # generalized Lyapunov equation
+
+ if (! isempty (c))
+ print_usage ();
+ endif
+
+ if (! is_real_square_matrix (a, b, e))
+ ## error ("lyap: a, b, e must be real and square");
+ error ("lyap: %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 ("lyap: a, b, e must have the same number of rows");
+ error ("lyap: %s, %s, %s must have the same number of rows", \
+ inputname (1), inputname (2), inputname (4));
+ endif
+
+ if (! issymmetric (b))
+ ## error ("lyap: b must be symmetric");
+ error ("lyap: %s must be symmetric", \
+ inputname (2));
+ endif
+
+ [x, scale] = slsg03ad (a, e, -b, false); # AXE' + EXA' = -B
+
+ ## x /= scale; # 0 < scale <= 1
+
+ otherwise
+ print_usage ();
+
+ endswitch
+
+ if (scale < 1)
+ warning ("lyap: solution scaled by %g to prevent overflow", scale);
+ endif
+
+endfunction
+
+
+## Lyapunov
+%!shared X, X_exp
+%! A = [1, 2; -3, -4];
+%! Q = [3, 1; 1, 1];
+%! X = lyap (A, Q);
+%! X_exp = [ 6.1667, -3.8333;
+%! -3.8333, 3.0000];
+%!assert (X, X_exp, 1e-4);
+
+## Sylvester
+%!shared X, X_exp
+%! A = [2.0 1.0 3.0
+%! 0.0 2.0 1.0
+%! 6.0 1.0 2.0];
+%!
+%! B = [2.0 1.0
+%! 1.0 6.0];
+%!
+%! C = [2.0 1.0
+%! 1.0 4.0
+%! 0.0 5.0];
+%!
+%! X = lyap (A, B, -C);
+%!
+%! X_exp = [-2.7685 0.5498
+%! -1.0531 0.6865
+%! 4.5257 -0.4389];
+%!
+%!assert (X, X_exp, 1e-4);
+
+## Generalized Lyapunov
+%!shared X, X_exp
+%! A = [ 3.0 1.0 1.0
+%! 1.0 3.0 0.0
+%! 1.0 0.0 2.0];
+%!
+%! E = [ 1.0 3.0 0.0
+%! 3.0 2.0 1.0
+%! 1.0 0.0 1.0];
+%!
+%! B = [-64.0 -73.0 -28.0
+%! -73.0 -70.0 -25.0
+%! -28.0 -25.0 -18.0];
+%!
+%! X = lyap (A.', -B, [], E.');
+%!
+%! X_exp = [-2.0000 -1.0000 0.0000
+%! -1.0000 -3.0000 -1.0000
+%! 0.0000 -1.0000 -3.0000];
+%!
+%!assert (X, X_exp, 1e-4);
+