Sampled-Data Synchronization under Matrix-Weighted Laplacian

In this paper, we study the synchronization problem of coupled identical electrical oscillators when the coupling between oscillators is described by matrices. In contrast to the mechanisms which make use of the instantaneous and the derivative information of the relative state, the sampled data technique is utilized to tackle the case when the derivative information of the relative state is unavailable. By transforming the proposed system into a first-order system, necessary and sufficient conditions are established for achieving synchronization of the oscillators under an undirected connected graph topology. Finally, simulation results are given to verify our theoretical results.