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authorShashank2017-05-29 12:40:26 +0530
committerShashank2017-05-29 12:40:26 +0530
commit0345245e860375a32c9a437c4a9d9cae807134e9 (patch)
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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