Adaptive event-triggered asynchronous control for T–S fuzzy systems with two-side looped-functional method

In this paper, we discuss the event-triggered $H_{\infty }$ control for T–S fuzzy systems with asynchronous premise variables, employing a two-side looped-functional method (TSLFM) to tackle this challenge. Firstly, we propose a fuzzy-dependent adaptive event-triggered mechanism (FDAETM) via aperiodic sampling, with the primary objective of minimizing the waste of communication resources. It is particularly noted that the FDAETM leads to asynchronous behavior between the premise variables of the fuzzy system and the controller. Secondly, to establish sufficient conditions for system stability, we introduce a TSLFM that incorporates sampling period information. Within the TSLFM framework, we make full use of the system state information from $x\left(t_c\right)$ to $x\left(t\right)$ and from $x\left(t\right)$ to $x\left(t_{c+1}\right)$, thereby deriving conditions that ensure the asymptotic stability of the system at the $H_{\infty }$ attenuation level. Compared to traditional Lyapunov functions, our proposed looped-functional method eliminates the need for positive definiteness and considers all information about the sampling interval, significantly reducing conservatism in the analysis. Finally, through two specific examples and comparative analysis, we demonstrate the effectiveness and advantages of the proposed method.