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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 [J]=fstabst(Stplant,r)
//[J]=fstabst(Stplant,r)
// Parametrization of all stabilizing feedbacks.
//-- Stplant=[ Stplant11 Stplant12;
// Stplant21 Stplant22]
// (in state-space or transfer form: conversion in state-space is
// done for the computations)
//-- r = size of Stplant22 subsystem (2,2) block of Stplant
//
// j =[ j11 j12;
// j21 j22]
// K is a stablizing controller iff K=LFT(J,r,Q) with Q stable
//!
if and(typeof(Stplant)<>["rational","state-space"]) then
error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"fstabst",1))
end
if Stplant.dt<>"c" then
error(msprintf(gettext("%s: Wrong type for argument #%d: In continuous time expected.\n"),"fstabst",1))
end
flag=0;
if typeof(Stplant)=="rational" then Stplant=tf2ss(Stplant),flag=1;end
[LHS,RHS]=argn(0);
[a,b1,b2,c1,c2,d11,d12,d21,d22]=smga(Stplant,r),
Rd1=d12'*d12,
R12=sqrtm(Rd1);
Rd2=d21*d21',
R22=sqrtm(Rd2);
p=r(2),r=r(1);
//-------------
[s1,s2,t]=size(Stplant);
[w1,k1]=rowcomp(d12),do1=w1(k1+1:s1-r,:)',
if do1==[] then do1=0,end,
[w2,k2]=rowcomp(d21'),do2=w2(k2+1:s2-p,:),
if do2==[] then do2=0,end,
//gains f and h
//-------------
ar1=a-b2*inv(Rd1)*d12'*c1,br1=b2*inv(Rd1)*b2',
cr1=c1'*do1*do1'*c1,
xc=riccati(ar1,br1,cr1,"cont"),
f=inv(Rd1)*(b2'*xc+d12'*c1),
ar2=(a-b1*d21'*inv(Rd2)*c2)',br2=c2'*inv(Rd2)*c2,
cr2=b1*do2'*do2*b1',
xo=riccati(ar2,br2,cr2,"cont"),
h=(b1*d21'+xo*c2')*inv(Rd2),
// J:
//---
aj=a-b2*f-h*c2+h*d22*f;
bj=[h ,(b2-h*d22)*inv(R12)],
cj=[-f;
-inv(R22)*(c2-d22*f)],
dj=[0*ones(p,r) eye(p,p)*inv(R12);
inv(R22)*eye(r,r) d22],
//Normalization to get inner and co-inner factors
J=syslin("c",aj,bj,cj,dj),
if flag==1 then J=ss2tf(J);end
endfunction
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