fstabst - Youla's parametrization
Parameterization of all stabilizing feedbacks.
P is partitioned as follows:
P=[ P11 P12; P21 P22]
(in state-space or transfer form: automatic conversion in state-space is done for the computations)
r = size of P22 subsystem, (2,2) block of P
J =[ J11 J12; J21 J22]
K is a stabilizing controller for P (i.e. P22 ) iff K=lft(J,r,Q) with Q stable.
The central part of J , J11 is the lqg regulator for P
This J is such that defining T as the 2-port lft of P and J : [T,rt]=lft(P,r,J,r) one has that T12 is inner and T21 is co-inner.
ny=2;nu=3;nx=4; P22=ssrand(ny,nu,nx); bigQ=rand(nx+nu,nx+nu);bigQ=bigQ*bigQ'; bigR=rand(nx+ny,nx+ny);bigR=bigR*bigR'; [P,r]=lqg2stan(P22,bigQ,bigR); J=fstabst(P,r); Q=ssrand(nu,ny,1);Q('A')=-1; //Stable Q K=lft(J,r,Q); A=h_cl(P,r,K); spec(A)
obscont , lft , lqg , lqg2stan ,