H∞ Control for Nonlinear Stochastic Systems: The Output-feedback Case

Abstract: In this paper we develop an H ∞ control theory, from the dissipation point of view, for a large class of time-continuous, stochastic, nonlinear, time-invariant systems with output-feedback. In particular, we introduce a notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems and we utilize it as a basis for the development of the theory. 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 the resulting closed-loop system dissipative. Stability, in probability and in the mean square sense, is discussed and sufficient conditions for achieving the stability and the H ∞ performance are introduced. Copyright c©2005 IFAC