H_infinity Control for Nonlinear Stochastic Systems: The Output-Feedback Case

In this paper we develop an H-infinity control theory, from the dissipation point of view, fora large class of time-continuous, stochastic, nonlinear, time-invariant systems withoutput-feedback. In particular, we introduce a notion of stochastic dissipative systems, analogously to the familiar notion of dissipationassociated with deterministic systems and we utilize it as a basis for the development of thetheory. In particular, we utilize the stochastic version of what is called Bounded Real Lemma(BRL) to synthesize an output-feedback controller. It is shown that this controller makes theresulting closed-loop system dissipative. Stability, in probability and in the mean square sense,is discussed and sufficient conditions for achieving the stability and the \hinf performance areintroduced.