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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 [P,m]=lqg2stan(P22,Q,R)
//P = standard plant for LQG control problem
//described by the triple (A,B,C)
// .
// x = Ax + w1 + Bu (resp x[n+1]= ... if dom='d')
//
// y = Cx + w2
//
// cov(w1,w2)=R;
//
// mininize (x,u)'Q(x,u)
//
flag=0;
P221=P22(1);
if P221(1)=="r" then
P22=tf2ss(P22);flag=1;end
P22=-P22;
[A,B,C,D22]=P22(2:5);
[nx,nu]=size(B);
[ny,nx]=size(C);
Qhalf=real(sqrtm(Q));
Rhalf=real(sqrtm(R));
B1=Rhalf(1:nx,:);D21=Rhalf(nx+1:nx+ny,:);
B2=B;
C1=Qhalf(:,1:nx);D12=Qhalf(:,nx+1:nx+nu);
C2=C;
D11=0*C1*B1;
dom=P22(7);
if dom==[] then
warning(msprintf(gettext("%s: Input argument #%d is assumed continuous time.\n"),"lqg2stan",1));
end
P=syslin(dom,A,real([B1,B2]),real([C1;C2]),real([D11,D12;D21,D22]));
m=size(C2*B2);
if flag==1 then
P=ss2tf(P);end
endfunction
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