Sliding mode control for T-S fuzzy delayed systems via event-triggered round-robin protocol

This study addresses the sliding mode control (SMC) issue for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay, which takes the access constrained communication network into account. Firstly, a new event-triggered round-robin (ETRR) protocol is designed to reduce the communication burden. Subsequently, according to the ETRR protocol, a new fuzzy mode-dependent SMC law is constructed, where the controller's membership functions (MFs) depend on the compromised triggered state. Furthermore, sufficient conditions related to the event-triggered mechanism are provided to ensure the stability of the controlled system with satisfactory $H_{\infty }$ performance and the reachability of the sliding surface by constructing a token-dependent Lyapunov functional. In addition, an optimization problem is established to solve the optimal $H_{\infty }$ performance level. Finally, the usefulness of the proposed SMC approach and the superiority of the ETRR protocol are displayed by comparative simulation experiments.