Cluster consensus on matrix-weighted switching networks

Abstract

This paper examines cluster consensus for multi-agent systems on matrix-weighted switching networks. Necessary and/or sufficient conditions under which cluster consensus can be achieved are obtained, as well as quantitative characterization of the steady-state of the cluster consensus. Specifically, when the underlying network switches amongst a finite number of networks, a necessary condition for cluster consensus on matrix-weighted switching networks is derived; moreover, it is shown that the steady-state of the nodes lies at the intersection of the null spaces of the matrix-valued Laplacians of the corresponding switching networks. Furthermore, when the underlying network switches amongst an infinite number of networks, the matrix-weighted integral network is employed to provide sufficient conditions for cluster consensus; analogous to the previous case, the quantitative characterization of the corresponding steady-state of the nodes pertains to the null space analysis of matrix-valued Laplacian of the “integral” network. Lastly, conditions for bipartite consensus of matrix-weighted switching networks are provided. Simulation examples demonstrate the presented theoretical results.