fstabst

Arguments

P

a continuous time linear dynamical system.

r

1x2 row vector, dimension of P22

J

a continuous time linear dynamical system (with same representation as P.

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.

Examples

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)

See also

• obscont — observer based controller
• lft — linear fractional transformation
• lqg — LQG compensator
• lqg2stan — LQG to standard problem

History