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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 [gm]=fspec(g)
// computes a spectral factorization:
// g = gtild(gm)*gm
//with stable gm and gm^-1 ( gm^-1 = invsyslin(gm) ).
//-- g: syslin list defining the linear system g
//-- gm:
//Assumptions:
//- g is invertible ( inv(D) exists ),
//- g and g^1 (invsyslin(g)) have no poles on the imaginary axis.
//- gtild(g) = g.
// (poles and zeros of g are symmetric wrt imaginary axis))
//- g(+oo) = D is positive definite.
//!
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"),"fspec",1))
end
if g.dt<>"c" then
error(msprintf(gettext("%s: Wrong type for argument #%d: In continuous time expected.\n"),"fspec",1))
end
flag=0;
if typeof(g)=="rational" then g=tf2ss(g),flag=1;end
[r1,r,d]=dtsi(g),[a,b,c]=r(2:4),
ari=a-b*inv(d)*c,
rri=b*inv(d)*b',qri=-c'*inv(d)*c,
x=riccati(ari,rri,qri,"c"),
id=sqrtm(d),
gm=syslin("c",a,b,inv(id)*(c+b'*x),id),
gm=minss(gm)
if flag==1 then gm=ss2tf(gm);end;
endfunction
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