A new integral sliding mode design method for nonlinear stochastic systems

Recently, several integral sliding mode control (ISMC) methodologies have been put forward to robust stabilization of nonlinear stochastic systems depicted by T-S fuzzy models. However, these results employ very restrictive assumptions on system matrices, which impose a great limitation to real applications. This paper aims to remove these assumptions and present a new ISMC method for fuzzy stochastic systems subjected to matched/mismatched uncertainties. To this end, a novel fuzzy integral sliding manifold function is adopted such that the matched uncertainties are completely rejected while the mismatched ones will not be enlarged during the sliding mode phase. Sufficient conditions are derived to ensure the stochastic stability of the closed-loop system under sliding motion. A fuzzy sliding mode controller is further presented to maintain the states of fuzzy stochastic system onto the predefined fuzzy manifold in the presence of uncertainties. The effectiveness and benefit of the developed new method are demonstrated by the inverted pendulum system.