Sliding Mode Control of T-S Fuzzy Systems Under Probabilistic Input Constraints

This work investigates the sliding mode control (SMC) problem of T-S fuzzy systems under probabilistic saturation constraints, where the actuator input is permitted to exceed its pre-given threshold with a certain probability. One obstacle is how to integrate the probabilistic saturation constraints into stability and reachability analysis considering the special structure of sliding mode controller. To address this problem, an SMC law is firstly synthesized by utilizing the well-known parallel distributed compensation scheme. Subsequently, we propose an altered sector condition incorporating the sign function and membership functions (MFS) to deal with the saturation nonlinearities. Facilitated by an auxiliary inequality, sufficient criteria are derived towards ensuring the local stochastic stability of the closed-loop system and the reachability of the prescribed sliding surface. A broader domain of stochastic stability may be anticipated through an optimization problem. Ultimately, a simulation example validates the efficacy of the provided control method.