Stochastic H∞ Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

Abstract

This paper is concerned with the stochastic H∞ state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedback H∞ controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribed H∞ performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.