Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay

The problem of delay-dependent robust fuzzy control for stochastic nonlinear systems with parameter uncertainties and time-varying delay is considered. A generalised Takagi-Sugeno fuzzy model is introduced to represent a stochastic nonlinear system in which the consequent parts are composed of a set of uncertain stochastic time-varying delay systems. Delay-dependent stability criterion is first obtained such that for all admissible uncertainties, the overall fuzzy system is asymptotically stable in the mean square. Then, based on the stability criterion and the parallel distributed compensation scheme, a state feedback fuzzy controller is proposed to guarantee the asymptotical stability in the mean square for the closed-loop system. These conditions are expressed in terms of linear matrix inequalities, and are dependent on the size of the time delay and on the size of the derivative of time delay. Finally, a simulation example is given to illustrate the effectiveness of the developed method.