Fuzzy Switching Sliding Mode Control of T-S Fuzzy Systems via an Event-Triggered Strategy

Two types of fuzzy switching sliding surfaces are presented, which combines an event-triggered (ET) method to investigate a fuzzy switching sliding mode control problem of T-S fuzzy systems. Different from the existing ET sliding mode control method, the fuzzy membership functions (FMFs) as well as their derivatives are fully employed for devising the fuzzy integral switching function. To reduce the frequency of controller updates, a corresponding triggering instant integral sliding variable is constructed, which is merely composed of variables related to the triggering instant. Meanwhile, a mixed ET mechanism is consist of fuzzy state variables errors and integral sliding variables errors, which serves as a critical element for ensuring the existence of a practical sliding mode (PSM). A bounded stability criteria of the sliding motion are derived using a fuzzy Lyapunov method, in which the linear decoupling strategies are applied to address a bilinear matrix inequality problem. Furthermore, a switching approach is employed to design the ET fuzzy switching SMC (ETFSSMC) law, which effectively utilizes the characteristics of the FMFs and their derivatives. According to the proposed ETFSSMC method, the existence of a PSM and no Zeno phenomenon can be guaranteed. In the end, the validity as well as the benefits of the methodology can be illustrated via two simulation examples.