Fuzzy Integral Sliding Mode Control with Switching Gains for Fuzzy Impulsive Systems

This paper studies the problem of a fuzzy integral sliding mode control (SMC) with switching gains for fuzzy impulsive systems with parametric uncertainties and unknown nonlinearity. To parametric uncertainties and unknown nonlinearity of the controlled system, a new fuzzy integral-based SMC approach is introduced. Compared with the traditional fuzzy integral SMC method, the sliding surface (SS) designed for fuzzy impulsive systems incorporates an additional impulsive component, aimed at preserving the continuity of the SS. Based on the designed fuzzy integral sliding surface, a fuzzy integral SMC law with switching gains is proposed to guarantee the attainment of the sliding surface at any specified time, and its switching gains is used to save resources by considering the different switching instants of the closed-loop systems. Then, by using the Lyapunov function theory and developing a time-varying Lyapunov function, the sufficient conditions to ensure exponential stability of the closed-loop system are established. Additionally, to convert the resulting nonlinear matrix inequalities into linear ones, a design algorithm for determining the control gains is formulated, leveraging the derived stability conditions and applying the Schur complement. Finally, by using an inverted pendulum as a simulation case, the efficiency of the constructed fuzzy integral SMC approach is proved.