Aperiodic Sampling-Based Event-Triggered $H_\infty$ Control for Interval Type-2 Fuzzy Systems via a Weakly Constrained Event-Triggered Functional

This article is dedicated to addressing the event-triggered $H_\infty$ control problem for interval type-2 fuzzy systems. A weakly constrained event-triggered functional is proposed by incorporating the event-triggering variable and $H_\infty$ performance index, which relaxes the restrictions imposed on Lyapunov functionals in existing sampled-data control studies. This functional also provides a graceful event-triggered $H_\infty$ analysis framework that avoids the use of the $S$-procedure. Then, the Lyapunov matrices in the functional are set to be aperiodic sampling-dependent, thereby further reducing the conservatism of the criteria. Furthermore, a basic-inequality-based method is provided to handle the imperfect premise matching between the fuzzy system and the fuzzy controller in interval type-2 fuzzy systems, avoiding the previous introduction of additional free matrices and extra constraints. Thereafter, the fuzzy controller design method is given, and the aperiodic sampling-based static/dynamic event-triggered control is effectively implemented. Ultimately, two case studies validate the effectiveness of the proposed approaches and demonstrate their ability to achieve superior event-triggered control effects compared with the existing literature.