Memory-Based Event-Triggered Control for Global Synchronization of Chaotic Lur’e Systems and Its Application

Abstract

In this article, a memory-based event-trigger (MBET) scheme is designed to investigate the global synchronization problem of a class of Lur’e systems. There are two reasons for presenting this issue: 1) most of the existing event-trigger schemes do not take the historical state information into account and, therefore, may have some conservatism in reducing the number of triggering times and 2) the existing Lyapunov functionals cannot be directly utilized in the stability analysis of the resulting closed-loop system in this article. Motivated by the above-mentioned considerations, an MBET scheme, in which a time-memory term and an exponential decaying term are incorporated into the threshold function, is newly designed. It is beneficial to enlarging the intertrigger intervals and, thus, can further reduce the transmission of sampled data packets. Taking the features of MBET into consideration, a novel piecewise but continuous functional is constructed. On this basis, Lyapunov stability theory and some inequality estimation techniques are used to develop three linear matrix inequalities (LMIs)-based synchronization criteria and, meanwhile, a co-design for the control gain and the triggering matrix is carried out. Finally, some comparative analyses are provided to demonstrate the advantages of the MBET through an example of Chua’s circuit. Also, the application to information safety is given to verify the effectiveness of the synchronization results by using a 3-neuron neural network.