h_inf

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

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

Version	Description
5.4.0	Sl is now checked for continuous time linear dynamical system. This modification has been introduced by this commit