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fstabst(1) Scilab Function 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('A')=-1; //Stable Q
K=lft(J,r,Q);
A=h_cl(P,r,K); spec(A)
SEE ALSO
obscont, lft, lqg, lqg2stan
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