Robust $maths\cr{H}_{\infty }$ Control for Stochastic T–S Fuzzy Systems via Integral Sliding-Mode Approach

In this paper, a novel dynamic integral sliding-mode control (ISMC) scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing ISMC approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities, and moreover, the sliding-mode controller can be obtained simultaneously. Simulation results from an inverted pendulum example illustrating the advantages and effectiveness of the proposed approaches are provided in the end.