Synchronization in Kuramoto Oscillator Networks With Sampled-Data Updating Law

In this article, we are concerned with the synchronization problem of Kuramoto oscillators under the sampled-data updating law. This article is motivated by the needs of synchronization of Kuramoto oscillators in the presence of periodic and asynchronous coupling updates. Based on the periodical sampled-data method, a sufficient condition ensuring synchronization under periodic updates is derived. In order to relax the requirement of having all data updated simultaneously, an event-triggered law is designed to implement asynchronous coupling updates. Our synchronization analysis does not rely on any linearization technique around equilibrium points. Instead, we employ the Lyapunov stability theory and nonsmooth analysis technique to deduce the synchronization conditions and estimate the region of attraction. The effectiveness of the proposed sampled-data coupling is illustrated by numerical simulations.