Sampled-data-based synchronization of matrix-weighted multi-layer complex networks via pinning control

Abstract

This paper examines the synchronization issue for a class of matrix-weighted multi-layer complex networks. Both intra-layer and inter-layer synchronization are investigated by means of sampled-data-based pinning control. In order to better describe the multidimensional attributes of state connection, matrix coupling rather than the conventional scalar weights is introduced to specify the node connections within and between layers. To reduce the waste of communication resources and save the control cost, a sampled-data-based pinning control strategy is designed to reach the intra-layer and inter-layer synchronization of matrix-weighted multi-layer complex networks. To effectively implement the pinning control, it is assumed that for each unpinned node (layer), there exists at least one pinned node (layer) which has a path to the unpinned node (layer). In this context, some sufficient conditions are derived through the utilization of algebraic graph theory, the Lyapunov stability theory, and a modified Halanay inequality. Finally, one simulation example is provided to verify the effectiveness of the obtained theoretical results.