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.