Asynchronous Control of Fuzzy Singularly Perturbed System With a Dynamic Event-Triggered Strategy
Kun Liang, Wangli He, Jing Xu
Abstract
This article is mainly concerned with the asynchronous control problem of fuzzy singularly perturbed systems (FSPSs) by designing an effective dynamic event-triggered control (ETC) strategy. Different from the existing results, a sample-based dynamic event-triggering condition related to the singular perturbation parameter (SPP) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> is proposed. Particularly, an auxiliary variable is employed in the event-triggered mechanism, which changes with the fluctuation of the system state. By constructing a novel parameter-dependent Lyapunov functional, some sufficient conditions are derived to stabilize FSPSs and solve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -dependent control gain. Furthermore, the upper bound of SPP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\bar{\varepsilon }$</tex-math></inline-formula> related with the proposed control gain is determined. The Zeno behavior can be naturally avoided by applying the sample-based dynamic ETC. Finally, two examples including a nonlinear circuit are presented to validate the effectiveness of obtained results.