Collective stochastic resonance behavior in the globally coupled fractional oscillator

This paper investigates the exponential synchronization of chaotic Lur’e systems (CLSs) with time-varying communication delays through event-triggered sampling control. Specially, first, a discrete event-triggered sampling control scheme, which only sends necessary sampling signal through the network, is designed for CLSs. By using this controller, the number of control updates could greatly reduce. Second, by getting utmost out of the usable information on the actual sampling pattern, some new sawtooth structure terms are introduced in the constructed Lyapunov–Krasovskii functional (LKF). It is worth mentioning that, different from some existing results to restrict the LKF to be positive define on the whole sampling intervals, the LKF is positive definite only needing at sampling times thanks to the use of the new inequality in Lemma 1. Third, less conservative synchronization criteria are established and the desired control gain matrix is obtained. Finally, two Chua’s circuit numerical simulations are presented to validate the feasibility and effectiveness of the theoretical results.