A Discontinuous Lyapunov Function Approach for Hybrid Event-Triggered Control of T–S Fuzzy Systems

This article addresses the
$H_{\infty }$
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.