h_inf¶

Continuous time H-infinity (central) controller

Calling Sequence¶

[Sk,ro]=h_inf(P,r,romin,romax,nmax)
[Sk,rk,ro]=h_inf(P,r,romin,romax,nmax)

:P a continuous-time linear dynamical system (“augmented” plant given: in state-space form or in transfer form)

: :r size of the P22 plant i.e. 2-vector [#outputs,#inputs] : :romin,romax a priori bounds on ro with ro=1/gama^2; ( romin=0

usually)

: :nmax integer, maximum number of iterations in the gama-iteration. :

h_inf computes H-infinity optimal controller for the continuous-time plant P.

The partition of P into four sub-plants is given through the 2-vector r which is the size of the 22 part of P.

P is given in state-space e.g. P=syslin(‘c’,A,B,C,D) with A,B,C,D = constant matrices or P=syslin(‘c’,H) with H a transfer matrix.

[Sk,ro]=H_inf(P,r,romin,romax,nmax) returns ro in [romin,romax] and the central controller Sk in the same representation as P.

(All calculations are made in state-space, i.e conversion to state- space is done by the function, if necessary).

Invoked with three LHS parameters,

[Sk,rk,ro]=H_inf(P,r,romin,romax,nmax) returns ro and the Parameterization of all stabilizing controllers:

a stabilizing controller K is obtained by K=lft(Sk,r,PHI) where PHI is a linear system with dimensions r’ and satisfy:

H_norm(PHI) < gamma. rk (=r) is the size of the Sk22 block and ro = 1/gama^2 after nmax iterations.

Algorithm is adapted from Safonov-Limebeer. Note that P is assumed to be a continuous-time plant.

F.Delebecque INRIA (1990)

Version Description 5.4.0 Sl is now checked for continuous time linear dynamical system. This modification has been introduced by this `commit`_ .. _gamitg: gamitg.html .. _commit: http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d .. _leqr: leqr.html .. _ccontrg: ccontrg.html