fstabst(1)

NAME
fstabst - Youla's parametrization

CALLING SEQUENCE
[J]=fstabst(P,r)

PARAMETERS

P   : syslin list (linear system)

r   : 1x2 row vector, dimension of P22

J   : syslin list (linear system in state-space representation)

DESCRIPTION
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.

EXAMPLE
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(2)=-1;  //Stable Q
A=H_cl(P,r,Q); spec(A)

SEE ALSO
obscont, lft, lqg, lqg2stan