Event-Triggered Control for Switched T–S Fuzzy Systems With General Asynchronism
Shuang Shi, Zhongyang Fei, Hamid Reza Karimi, Hak‐Keung Lam
Abstract
In this article, the problem of event-triggered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> control design is investigated for a class of continuous-time switched Takagi–Sugeno (T–S) fuzzy systems. Specifically, the nonweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance is guaranteed for the system with mode-dependent average dwell-time (MDADT) switching, which is more general than the weighted one in most existing results. Meanwhile, the existence of asynchronous phenomenon between event-triggered instants is taken into account, which is more practical and complicated in the system under consideration. It is compulsive in most existing results that the candidate controllers are synchronous with the subsystems, while this constraint is released to deal with the case that the system switches more than once between two adjacent event-trigger instants. First of all, by verifying the existence of the minimal inter-execution time, it is demonstrated that the adopted event-triggered mechanism can exclude the Zeno behavior. Next, an improved criterion on stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance is derived for switched T–S fuzzy systems with MDADT switching. On this basis, the mode-dependent event-triggered mechanism and controllers are co-designed. Finally, two simulations are provided to illustrate the effectiveness of the developed event-triggered control scheme.