LAUSR

In this paper, we study the synchronization problem of identical oscillators interacting via matrix-weighted couplings under both undirected and directed graph topologies. In contrast to the existing mechanism which makes 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. Necessary and sufficient conditions depending on the coupling gains, the sampling period, and the spectra of the matrix-weighted Laplacian, are established for achieving synchronization of the oscillators under undirected and directed graph topologies. The constraints on the matrix weights that guarantee the desired spectral property of the Laplacian are also investigated. Finally, simulation results are given to verify our theoretical results.