$H_\infty$ 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.

I. Introduction

Lur'e system is a typical kind of nonlinear system. Chaotic Lur'e system is the Lur'e system that displays chaotic dynamics. In fact, many chaotic systems, such as n-scroll attractors [1], Chua's circuits [2], and chaotic neural networks [3] can be expressed as a Lur'e form. It consists of a linear system coupled with some nonlinear terms. Since the pioneering work of Carroll and Pecora [4], the study on synchronization of chaotic systems has attracted extensive concern in recent years because of its wide applications in the fields of secure communication, information science, image processing, and chemical reaction. Moreover, time-delay is a common phenomenon in practical systems, which may bring about instability or the situation that the system performance will deteriorate significantly. So far, many control methods for master–slave synchronization of chaotic Lur'e systems have been developed, such as delay feedback control [5], impulsive control [6], and adaptive control [7], [8]. It is noteworthy that most of these control methods are based on continuous measurements. With the integration of communication networks, these continuous measure schemes will lead to redundant sampled data and will consume limited network bandwidth a lot.