h_inf

Arguments

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.

Description

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 for continuous time systems
• ccontrg — Central H-infinity continuous time controller
• leqr — H-infinity LQ gain (full state)

Authors

F.Delebecque INRIA (1990)

History