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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 [X1,X2,zero]=ric_desc(H,E)
//[X1,X2,zero]=ric_desc(H [,E]) Descriptor Riccati solver with
// hamiltonian matrices as inputs.
// (see also riccati)
//In the continuous time case calling sequence is ric_desc(H) (one input).
// Riccati equation is:
// (Ec) A'*X + X*A + X*R*X -Q = 0.
// Defining the hamiltonian matrix H by:
// H = [A R;
// Q -A']
// with [X1,X2,err]=ric_desc(H),solution X is given by X=X1/X2.
// zero=norm 1 of lhs of (Ec)
//
// (solution X is also given by X=riccati(A,Q,R,'c'))
//
//
//In the discrete-time case calling sequence is ric_desc(H,E) (two inputs).
// Riccati solution is:
// (Ed) A'*X*A-(A'*X*B*(R+B'*X*B)^-1)*(B'*X*A)+C-X = 0.
//
// Defining G=B/R*B' and the hamiltonian pencil (E,H) by:
// E=[eye(n,n),G;
// 0*ones(n,n),A']
//
// H=[A, 0*ones(n,n);
// -C, eye(n,n)];
// with [X1,X2,err]=ric_desc(H,E),solution X is given by X=X1/X2.
// zero=norm 1 of lhs of (Ed)
//
// (solution X is also given by X=riccati(A,G,C,'d') with G=B/R*B')
//!
[LHS,RHS]=argn(0);
if RHS==1 then
[n2,n2]=size(H);
n1=n2/2;
A=H(1:n1,1:n1);
//R=H(1:n1,n1+1:n2); Q=H(n1+1:n2,1:n1);
[Hb,W1]=bdiag(H);
if cond(W1) > 1.d10*norm(H,1) then
// write(%io(2),'Warning : Bad conditioning => balancing');
[Hb,W1]=balanc(H);
end
if cond(W1) > 1.d+10*norm(H,1) then Hb=H,W1=eye(W1);end
[W2,n]=schur(Hb,"c");Hb=[]
if n<>n1 then mprintf(gettext("%s: Stationary Riccati solver failed.\n"),"ric_desc");end
W1=W1*W2;W2=[]
UV=W1(:,1:n1);W1=[]
X2=UV(1:n1,:);X1=UV(n1+1:n2,:);UV=[];
if n<>n1 then
X2=eye(n1,n1);X1=0;
end
zr=X2'*A'*X1+X1'*A*X2+X1'*H(1:n1,n1+1:n2)*X1-X2'*H(n1+1:n2,1:n1)*X2;
zero=norm(zr,1);
end
if LHS==1 then X1=X1/X2;end
if RHS==2 then
[n2,n2]=size(H);n1=n2/2;
n1=n2/2;
[UV,n]=schur(H,E,"d");
X2=UV(1:n,1:n);X1=UV(n+1:2*n,1:n);
if LHS==3 then
A=H(1:n1,1:n1);G=E(1:n,n+1:2*n);C=-H(n+1:2*n,1:n);B=real(sqrtm(G));R=eye(A);
X=X1/X2;zero=A'*X*A-(A'*X*B/(R+B'*X*B))*(B'*X*A)+C-X;
end
end
if LHS==1 then X=X1/X2;end
endfunction
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