Dissipativity based H∞ control for nonlinear stochastic systems with time-varying delays

This paper is concerned with the H_∞ state feedback control problem for a class of nonlinear stochastic systems with time-varying state delays. Firstly, the stochastic dissipativity of the time-delay nonlinear system is established, based on which the H_∞ state feedback controller is synthesized. We show that the closed-loop system rendered by the designed controller can achieve the L₂-gain performance and exponential stability in the sense of mean square. Finally, these sufficient conditions are further specialized as solving a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) for a class of special stochastic nonlinear delayed systems.