Delay-dependent state-feedback H_∞ control for nonlinear stochastic systems with time-varying delays

This paper is concerned with the state-feedback H_∞ control problem for a class of stochastic nonlinear systems with time-varying state delays, where both the disturbance and the white noise are considered. To synthesize the investigated system, the parameter-dependent storage functional is firstly constructed. By means of completing the square, the delay-dependent controller is designed such that the closed-loop system is exponentially stable in mean square and the prescribed disturbance attenuation level is achieved. Finally, the developed delay-dependent conditions are further specialized to synthesize a type of special delayed nonlinear systems by solving several linear matrix inequalities (LMIs) and a bilinear matrix inequality (BMI).