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.

Automated summary

This article examines the consensus problem on matrix-weighted undirected switching networks, providing conditions for achieving average consensus and discussing necessary and sufficient conditions for reaching average consensus in periodic matrix-weighted switching networks from an algebraic perspective. Simulation results are provided to demonstrate the theoretical analysis.