Observer-based L2–L∞ control for a class of stochastic systems with time-varying delay

This paper is devoted to the problem of L₂-L_∞ control for a class of stochastic time-delay systems via observer-based feedback control. The considered observer contains no time-delay. The purpose is to design an observer-based feedback stabilizing controller such that the augmented closed-loop system is stochastically asymptotically stable with a prescribed L₂-L_∞ performance satisfied. Based on the stochastic stability theory, a delay-dependent sufficient condition is derived in terms of linear matrix inequalities (LMIs). The observer and controller design method is proposed, while the corresponding explicit expression for the observer and controller gain matrices is also given. Finally, numerical examples and simulation results are included to illustrate the effectiveness of the proposed results.