index ad3499d..160501f 100644 (file)
@@ -115,31 +115,48 @@ X=F'*X*F-F'*X*G1*((G2+G1'*X*G1)^-1)*G1'*X*F+H
<title>Examples</title>
<programlisting role="example"><![CDATA[
//Standard formulas to compute Riccati solutions
-A=rand(3,3);B=rand(3,2);C=rand(3,3);C=C*C';R=rand(2,2);R=R*R'+eye();
+A=rand(3,3);
+B=rand(3,2);
+C=rand(3,3);
+C=C*C';
+R=rand(2,2);
+R=R*R'+eye();
B=B*inv(R)*B';
X=ricc(A,B,C,'cont');
norm(A'*X+X*A-X*B*X+C,1)
H=[A -B;-C -A'];
-[T,d]=schur(eye(H),H,'cont');T=T(:,1:d);
+[T,d]=schur(eye(H),H,'cont');
+T=T(:,1:d);
X1=T(4:6,:)/T(1:3,:);
norm(X1-X,1)
-[T,d]=schur(H,'cont');T=T(:,1:d);
+[T,d]=schur(H,'cont');
+T=T(:,1:d);
X2=T(4:6,:)/T(1:3,:);
norm(X2-X,1)
//       Discrete time case
-F=A;B=rand(3,2);G1=B;G2=R;G=G1/G2*G1';H=C;
+F=A;
+B=rand(3,2);
+G1=B;
+G2=R;
+G=G1/G2*G1';
+H=C;
X=ricc(F,G,H,'disc');
norm(F'*X*F-(F'*X*G1/(G2+G1'*X*G1))*(G1'*X*F)+H-X)
H1=[eye(3,3) G;zeros(3,3) F'];
H2=[F zeros(3,3);-H eye(3,3)];
-[T,d]=schur(H2,H1,'disc');T=T(:,1:d);X1=T(4:6,:)/T(1:3,:);
+[T,d]=schur(H2,H1,'disc');
+T=T(:,1:d);
+X1=T(4:6,:)/T(1:3,:);
norm(X1-X,1)
Fi=inv(F);
Hami=[Fi Fi*G;H*Fi F'+H*Fi*G];
-[T,d]=schur(Hami,'d');T=T(:,1:d);
+[T,d]=schur(Hami,'d');
+T=T(:,1:d);
Fit=inv(F');
Ham=[F+G*Fit*H -G*Fit;-Fit*H Fit];
-[T,d]=schur(Ham,'d');T=T(:,1:d);X2=T(4:6,:)/T(1:3,:);
+[T,d]=schur(Ham,'d');
+T=T(:,1:d);
+X2=T(4:6,:)/T(1:3,:);
norm(X2-X,1)
]]></programlisting>
</refsection>