Event-Triggered Sliding-Mode Control for Polynomial Fuzzy Singular Systems

This article focuses on the problem of the observer-based sliding-mode control (SMC) for polynomial fuzzy singular systems via a novel dynamic event-triggered (DET) mechanism. First, the DET mechanism is introduced to reduce the transmission burden in the communication network. Second, the DET-based observer is constructed to estimate the unavailable state variables. On this basis, the integral sliding variable is provided, and the observer dynamics can be obtained. A sufficient condition is then proposed to make sure that the whole closed-loop system composed of the observer dynamics and the estimation error system is admissible and passive by utilizing the sum-of-squares approach. Meanwhile, the sliding surface parameter matrix, the observer gain, and the trigger weighting matrix are co-designed. It should be emphasized that the common equality constraints, nonstrict and nonlinear inequality constraints are removed through equivalent sets and several inequality techniques in this design process. Moreover, the DET observer-based SMC law is derived to assure the reachability of the specified sliding surface. Finally, the theoretical results are verified by simulation results.