Youla’s parametrization of continuous time linear dynmaical systems
J = fstabst(P,r)
: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.
:
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)
Version Description 5.4.0 Sl is now checked for continuous time linear dynamical system. This modification has been introduced by this `commit`_ .. _obscont: obscont.html .. _lqg2stan: lqg2stan.html .. _lft: lft.html .. _lqg: lqg.html .. _commit: http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d