A Discontinuous Lyapunov Function Approach for Hybrid Event-Triggered Control of T–S Fuzzy Systems
针对T-S模糊系统，提出一种混合事件触发控制策略，结合自适应调整减少数据传输并排除Zeno行为，通过构造不连续Lyapunov函数和引理，研究指数稳定性和干扰抑制性能，并给出稳定性与控制设计的充分条件。
This article addresses the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control issue for Takagi–Sugeno (T–S) fuzzy systems via an event-triggered control mechanism. First, a hybrid event-triggered control strategy combined with an adaptively adjusted approach is proposed, by which the data transmission can be effectively reduced, and meanwhile, the Zeno behavior is excluded. Then, a discontinuous Lyapunov function is constructed for the resulting hybrid event-triggered control system, and a novel lemma is developed for studying the exponential stability and disturbance attenuation performance. By utilizing a time-varying variable to manage the error during the interevent intervals together with using the newly proposed lemma, sufficient criteria are established for the stability and control design of the event-triggered T–S fuzzy system with the imperfect premise matching. Finally, numerical simulations are presented to illustrate the usefulness and advantages of the obtained theorems.