Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / @lti / norm.m

diff --git a/octave_packages/control-2.3.52/@lti/norm.m b/octave_packages/control-2.3.52/@lti/norm.m
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+## Copyright (C) 2009, 2010, 2011   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{gain} =} norm (@var{sys}, @var{2})
+## @deftypefnx {Function File} {[@var{gain}, @var{wpeak}] =} norm (@var{sys}, @var{inf})
+## @deftypefnx {Function File} {[@var{gain}, @var{wpeak}] =} norm (@var{sys}, @var{inf}, @var{tol})
+## Return H-2 or L-inf norm of LTI model.
+##
+## @strong{Algorithm}@*
+## Uses SLICOT AB13BD and AB13DD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: November 2009
+## Version: 0.5
+
+function [gain, varargout] = norm (sys, ntype = "2", tol = 0.01)
+
+  if (nargin > 3)                     # norm () is caught by built-in function
+    print_usage ();
+  endif
+
+  if (is_real_scalar (ntype))
+    if (ntype == 2)
+      ntype = "2";
+    elseif (isinf (ntype))
+      ntype = "inf";
+    else
+      error ("lti: norm: invalid norm type");
+    endif
+  elseif (ischar (ntype))
+    ntype = lower (ntype);
+  else
+    error ("lti: norm: invalid norm type");
+  endif
+
+  switch (ntype)
+    case "2"
+      gain = h2norm (sys);
+
+    case "inf"
+      [gain, varargout{1}] = linfnorm (sys, tol);
+
+    otherwise
+      error ("lti: norm: invalid norm type");
+  endswitch
+
+endfunction
+
+
+function gain = h2norm (sys)
+
+  if (isstable (sys))
+    [a, b, c, d] = ssdata (sys);
+    discrete = ! isct (sys);
+    if (! discrete && any (d(:)))     # continuous and non-zero feedthrough
+      gain = inf;
+    else
+      gain = slab13bd (a, b, c, d, discrete);
+    endif
+  else
+    gain = inf;
+  endif
+
+endfunction
+
+
+function [gain, wpeak] = linfnorm (sys, tol = 0.01)
+
+  [a, b, c, d, e, tsam, scaled] = dssdata (sys, []);
+  discrete = ! isct (sys);
+  tol = max (tol, 100*eps);
+  
+  if (isempty (e))
+    [fpeak, gpeak] = slab13dd (a, a, b, c, d, discrete, false, tol, scaled);  # TODO: avoid dummy argument
+  else
+    if (rcond (e) < eps)
+      gain = inf;
+      wpeak = inf;
+      return;
+    else
+      [fpeak, gpeak] = slab13dd (a, e, b, c, d, discrete, true, tol, scaled);
+    endif
+  endif
+  
+  if (fpeak(2) > 0)
+    if (discrete)
+      wpeak = fpeak(1) / abs (tsam);  # tsam could be -1
+    else
+      wpeak = fpeak(1);
+    endif
+  else
+    wpeak = inf;
+  endif
+  
+  if (gpeak(2) > 0)
+    gain = gpeak(1);
+  else
+    gain = inf;
+  endif
+
+endfunction
+
+
+## norm ct
+%!shared H2, Hinf
+%! sys = ss (-1, 1, 1, 0);
+%! H2 = norm (sys, 2);
+%! Hinf = norm (sys, inf);
+%!assert (H2, 0.7071, 1.5e-5);
+%!assert (Hinf, 1, 5e-4);
+
+
+## norm dt
+%!shared H2, Hinf
+%! a = [ 2.417   -1.002    0.5488
+%!           2        0         0
+%!           0      0.5         0 ];
+%! b = [     1
+%!           0
+%!           0 ];
+%! c = [-0.424    0.436   -0.4552 ];
+%! d = [     1 ];
+%! sys = ss (a, b, c, d, 0.1);
+%! H2 = norm (sys, 2);
+%! Hinf = norm (sys, inf);
+%!assert (H2, 1.2527, 1.5e-5);
+%!assert (Hinf, 2.7, 0.1);