On multi-consensus and almost equitable graph partitions

Abstract

This paper deals with multi-consensus in multi-agent systems, focusing on the relationship between multi-consensusability and the underlying digraph topology. In particular, the topological arrangement of the network nodes naturally suggests distinguishing among, on the one hand, separate independent groups of agents agreeing internally and, on the other hand, a dependent common subgraph whose internal consensuses can be computed as a convex combination of the different consensuses achieved by the previously mentioned independent groups. The distinct achieved consensuses are as many as the number of groups of agents defining cells of a suitable almost equitable partition. Despite the notational complexity, the related computations are quite simple to carry out, as shown in some examples.