--- /dev/null
+## 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);