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## Copyright (C) 1996, 1998, 2000, 2002, 2004, 2005, 2006, 2007
## Auburn University. All rights reserved.
##
##
## This program 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.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} h2norm (@var{sys})
## Computes the
## @iftex
## @tex
## $ { \cal H }_2 $
## @end tex
## @end iftex
## @ifinfo
## H-2
## @end ifinfo
## norm of a system data structure (continuous time only).
##
## Reference:
## Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions to Standard}
## @iftex
## @tex
## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-2 and H-infinity}
## @end ifinfo
## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
## @end deftypefn
## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: August 1995
## updated for system data structure by John Ingram November 1996
function h2gain = h2norm (sys)
if (nargin != 1)
print_usage ();
elseif (! isstruct (sys))
error ("Sys must be in system data structure");
endif
dflg = is_digital (sys);
if (! is_stable (sys))
warning ("h2norm: unstable input system; returning Inf");
h2gain = Inf;
else
## compute gain
[a, b, c, d] = sys2ss (sys);
if (dflg)
M = dlyap (a, b*b');
else
M = lyap (a, b*b');
endif
if (min (real (eig (M))) < 0)
error ("h2norm: gramian not >= 0 (lightly damped modes?)")
endif
h2gain = sqrt (trace (d*d' + c*M*c'));
endif
endfunction
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