New Approach to General Nonlinear Discrete-Time Stochastic $H_{\infty }$ Control

Abstract

In this paper, a new approach based on convex analysis is introduced to solve the $H_{\infty }$ problem for discrete-time nonlinear stochastic systems. A stochastic version of bounded real lemma is proved and the state feedback $H_{\infty }$ control is studied. Two examples are presented to show the effectiveness of our developed theory.

29 pages, 4 figures, 36 references