Exponential Synchronization of Chaotic Lur’e Systems Using an Adaptive Event-Triggered Mechanism

This paper investigates event-triggered exponential synchronization of master-slave chaotic Lur'e systems (CLSs). First, in order to save communication resources, a novel event-based transmission strategy is developed using continuous-time measurements while a positive minimum inter-event time can be ensured. Second, an adaptive law is adopted to adjust dynamically the event-triggered threshold parameter. Compared with some existing static event-triggered mechanisms, the proposed event-triggered mechanism can provide a better tradeoff between communication resource saving and desired synchronization performance. Third, a switched Lyapunov-Krasovskii functional (LKF) is introduced, which is continuous at the switching instants but not necessarily positive definite at sampling intervals. This LKF is employed to derive a less conservative synchronization criterion for CLSs, based on which, the synchronization controller gain and the event-triggered parameters can be co-designed in terms of linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to illustrate the efficiency of the proposed method.