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

This paper is concerned with the stochastic 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 controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribed performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

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