From Matrix-Weighted Consensus to Multipartite Average Consensus

This article studies a consensus protocol, which is called a multipartite average consensus, of a multiagent system over signed undirected networks in which all agents could be partitioned into multiple subgroups and all agents in the same group converge to the average of their initial values. The proposed protocol is based on results from a matrix-weighted consensus. It is shown that a matrix-weighted consensus can be transformed into a multipartite average consensus. We then discuss a method to combine some subgroups or all subgroups into a union group in order that all agents in the union group reach an average consensus. Finally, we provide examples and simulations to validate the statement.