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Scilab help >> CACSD > h_inf


H-infinity (central) controller

Calling Sequence




syslin list : continuous-time linear system (``augmented'' plant given in state-space form or in transfer form)


size of the P22 plant i.e. 2-vector [#outputs,#inputs]


a priori bounds on ro with ro=1/gama^2; (romin=0 usually)


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.

See Also

  • gamitg — H-infinity gamma iterations
  • ccontrg — central H-infinity controller
  • leqr — H-infinity LQ gain (full state)


F.Delebecque INRIA (1990)

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Last updated:
Thu Mar 03 10:59:40 CET 2011