Robust Integral Sliding Mode Control for Fuzzy Stochastic Impulsive Systems

This paper investigates the sliding mode control problem for Takagi–Sugeno (T–S) fuzzy stochastic impulsive systems. Since considered T–S fuzzy systems contain stochastic impulses, a new continuous fuzzy integral sliding surface is designed so that its reachability is ensured for any a given time. Based on the designed fuzzy integral sliding surface, a fuzzy sliding mode controller is developed, which can guarantee the exponential stability of T–S fuzzy stochastic impulsive system. By constructing an appropriate Lyapunov function, the exponential stability conditions of T–S fuzzy stochastic impulsive systems are established in the form of linear matrix inequalities. Consequently, a control design algorithm is formulated based on the established the exponential stability conditions. Finally, two simulation examples and comparisons are provided to check the effectiveness of the proposed fuzzy SMC scheme.