Analysis of Cluster Consensus in Continuous-Time Networks

In this paper, we investigate the cluster consensus problem for multi-agent systems in continuous-time. As opposed to existing literature, we do not assume that the clusters are pre-determined. The main contribution of the paper is to determine the number of clusters for a network of agents whose interactions are modelled via a directed graph. The results are obtained by using primary & secondary layer subgraphs and extension of Laplacian matrices. Finally, the results are illustrated via several numerical examples.