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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA -
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function [nh]=h2norm(g,tol)
//
// /+00
// 2 | *
// |g| =1/(2*%pi).|trace[g(jw).g(jw)]dw
// 2 |
// /-00
if argn(2)<1 then
error(msprintf(gettext("%s: Wrong number of input argument(s): At least %d expected.\n"),..
"h2norm",1))
end
if type(g)==1,if norm(g)==0,nh=0,return,end,end,
if and(typeof(g)<>["rational","state-space"]) then
error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"h2norm",1))
end
if g.dt<>"c" then
error(msprintf(gettext("%s: Wrong type for argument #%d: In continuous time expected.\n"),"h2norm",1))
end
[lhs,rhs]=argn(0),
if rhs==1 then
tol=1000*%eps,
else
if type(tol)<>1|size(tol,"*")<>1 then
error(msprintf(gettext("%s: Wrong type for input argument: Scalar expected.\n"),"h2norm",2))
end
if ~isreal(tol)|tol<=0 then
error(msprintf(gettext( "%s: Input argument #%d must be strictly positive.\n"),"h2norm",2))
end
end;
select typeof(g)
case "state-space" then
if norm(g.D)>0 then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Proper system expected.\n"),"h2norm",1)),
end;
sp=spec(g.A),
if max(real(sp))>=-tol then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Stable system expected.\n"),"h2norm",1)),
end,
w=obs_gram(g.A,g.C,"c"),
nh=abs(sqrt(sum(diag(g.B'*w*g.B)))),return,
case "rational" then
num=g.num;
den=g.den;
s=poly(0,varn(den)),
[t1,t2]=size(num),
for i=1:t1,
for j=1:t2,
n=num(i,j),d=den(i,j),
if coeff(n)==0 then
nh(i,j)=0,
else
if degree(n)>=degree(d) then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Proper system expected.\n"),"h2norm",1)),
end
pol=roots(d),
if max(real(pol))>-tol then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Stable system expected.\n"),"h2norm",1)),
end,
nt=horner(n,-s),dt=horner(d,-s),
nh(i,j)=residu(n*nt,d,dt),
end,
end
end
nh=sqrt(sum(nh)),return,
end
endfunction
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