$H_\infty$ Exponential Synchronization of Chaotic Lur'e Systems: An Asynchronous Memory-Based Event-Triggered Scheme

This article studies the
$H_\infty$
exponential synchronization problem of delayed chaotic Lur'e systems (DCLSs). Considering the case of sensors sampling with different periods, an asynchronous memory-based event-triggered scheme is proposed to deal with the multiple sampling periods cases. To be specific, a group of memory-based event-triggered processors with different triggering conditions are set behind the sensors. Such a scheme supports the sensors to sample with different periods and supports the packets arrive at the controller side asynchronously. Then, to develop the closed-loop system, a merging time sequence
$\lbrace t_{s}\rbrace$
is constituted by using the release instants and by considering the transmission delays. On this basis, a so-called multirate Lyapunov functional is constructed, which including the information of the sampling upper bounds of different sensors. Furthermore, two criteria for
$H_\infty$
exponential synchronization of DCLSs are derived in the form of linear matrix inequalitys (LMIs). And, the controller gain can be obtained from the feasible solution of the LMIs. And, a numerical example is provided to demonstrate the effectiveness and merits of the proposed method.