Distributed Event-Triggered Control of Large-Scale Fuzzy Systems With Long Transmission Delays

This article develops a novel hybrid system approach to address the event-triggered stabilization problem of large-scale Takagi–Sugeno (T–S) fuzzy systems subject to variable long transmission delays. Various changing behaviors of deviation errors caused by transmission delays, as well as the changes of some auxiliary variables, are modeled by a hybrid dynamical system with flow dynamics and jump dynamics. Then, under the hybrid control framework, an observer-based antidisturbance controller and a delay-independent hybrid event-triggering mechanism (HETM) are proposed to stabilize the closed-loop system, while guaranteeing desired performance in disturbance attenuation and delay tolerance. Compared with the case where small transmission delays could naturally lead to delay-independent HETM, the long transmission delays pose many difficulties. Given this, we propose a more robust triggering condition with only using several memorized previous states to guarantee the HETM to be delay-independent even in case of long transmission delays. Moreover, the obtained stability conditions avoid involving lower and upper bounds of transmission delays in matrix inequalities, so they can be delay-independent and significantly simplified. Relationships between system stability and maximally allowable transmission delay are transformed into designing proper auxiliary functions offline. Finally, the effectiveness of the proposed control protocol is demonstrated by a numerical example.