STOCHASTIC H-INFINITY

We consider stochastic linear plants which are controlled by dynamic o utput feedback and subjected to both deterministic and stochastic pert urbations. Our objective is to develop an H-infinity-type theory for s uch systems. We prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations. This enables us to obtain necessary and sufficient conditions for the existence of a stabilizin g compensator which keeps the effect of the perturbations on the to-be -controlled output below a given threshhold gamma > 0. In the determin istic case, the analogous conditions involve two uncoupled linear matr ix inequalities, but in the stochastic setting we obtain coupled nonli near matrix inequalities instead. The connection between H-infinity th eory and stability radii is discussed and leads to a lower bound for t he radii, which is shown to be tight in some special cases.