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## Copyright (C) 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{hsv} =} hsvd (@var{sys})
## @deftypefnx{Function File} {@var{hsv} =} hsvd (@var{sys}, @var{"offset"}, @var{offset})
## @deftypefnx{Function File} {@var{hsv} =} hsvd (@var{sys}, @var{"alpha"}, @var{alpha})
## Hankel singular values of the stable part of an LTI model. If no output arguments are
## given, the Hankel singular values are displayed in a plot.
##
## @strong{Algorithm}@*
## Uses SLICOT AB13AD by courtesy of
## @uref{http://www.slicot.org, NICONET e.V.}
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Created: January 2010
## Version: 0.4
function hsv_r = hsvd (sys, prop = "offset", val = 1e-8)
if (nargin != 1 && nargin != 3)
print_usage ();
endif
if (! isa (sys, "lti"))
error ("hsvd: first argument must be an LTI system");
endif
if (! is_real_scalar (val))
error ("hsvd: third argument must be a real scalar");
endif
[a, b, c, ~, ~, scaled] = ssdata (sys);
discrete = ! isct (sys);
switch (tolower (prop(1)))
case "o" # offset
if (discrete)
alpha = 1 - val;
else
alpha = - val;
endif
case "a" # alpha
alpha = val;
otherwise
error ("hsvd: second argument invalid");
endswitch
[hsv, ns] = slab13ad (a, b, c, discrete, alpha, scaled);
if (nargout)
hsv_r = hsv;
else
bar ((1:ns) + (rows (a) - ns), hsv);
title (["Hankel Singular Values of Stable Part of ", inputname(1)]);
xlabel ("State");
ylabel ("State Energy");
grid ("on");
endif
endfunction
%!shared hsv, hsv_exp
%! a = [ -0.04165 0.0000 4.9200 -4.9200 0.0000 0.0000 0.0000
%! -5.2100 -12.500 0.0000 0.0000 0.0000 0.0000 0.0000
%! 0.0000 3.3300 -3.3300 0.0000 0.0000 0.0000 0.0000
%! 0.5450 0.0000 0.0000 0.0000 -0.5450 0.0000 0.0000
%! 0.0000 0.0000 0.0000 4.9200 -0.04165 0.0000 4.9200
%! 0.0000 0.0000 0.0000 0.0000 -5.2100 -12.500 0.0000
%! 0.0000 0.0000 0.0000 0.0000 0.0000 3.3300 -3.3300];
%!
%! b = [ 0.0000 0.0000
%! 12.5000 0.0000
%! 0.0000 0.0000
%! 0.0000 0.0000
%! 0.0000 0.0000
%! 0.0000 12.500
%! 0.0000 0.0000];
%!
%! c = [ 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
%! 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000];
%!
%! sys = ss (a, b, c, [], "scaled", true);
%! hsv = hsvd (sys, "alpha", 0.0);
%!
%! hsv_exp = [2.5139; 2.0846; 1.9178; 0.7666; 0.5473; 0.0253; 0.0246];
%!
%!assert (hsv, hsv_exp, 1e-4);
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