Synchronization of Kuramoto-oscillator networks under event-triggered impulsive control with noise perturbation

This paper studies the stochastic average synchronization of Kuramoto-oscillator networks under event-triggered impulsive control (ETIC) strategies, in which the event-triggered mechanism (ETM) determines the impulsive control time sequence. The continuous ETM is designed to avoid the Zeno behavior by continuous measuring, and the periodic ETM is proposed by periodic sampling. Based on the proposed ETIC methods, several sufficient conditions for the stochastic average synchronization of Kuramoto-oscillator networks are established. Unlike time-triggered impulsive control, where the triggered instants are pre-designed, ETIC is activated only upon the occurrence of an event, so synchronization conditions are heavily dependent on the ETM. Furthermore, there is no control input between two successive triggering instants, and the control input is required only at the trigger instants. Finally, numerical simulations are shown to illustrate the effectiveness of the theoretical results. Besides, it is found that the presence of noise may favor the synchronization of Kuramoto-oscillator networks.