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

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