Consensus on Matrix-Weighted Switching Networks

This article examines the consensus problem on matrix-weighted undirected switching networks. First, we introduce the matrix-weighted integral network for analyzing such networks. Under mild assumptions on the switching pattern of a sequence of networks, conditions under which average consensus can be achieved are then provided. It is shown that for matrix-weighted switching networks, the existence of a positive spanning tree in the associated integral network plays a crucial role in achieving average consensus. In particular, for periodic matrix-weighted switching networks, necessary and sufficient conditions for reaching average consensus is obtained from an algebraic perspective. Simulation results are provided to demonstrate the theoretical analysis.