Consensus of Multi-Agent Systems in Clustered Networks

This paper deals with the consensus problem in networks divided into subnetworks (also called clusters), where each node of the network represents an agent with linear dynamics. Each subnetwork is represented by a fixed and directed graph. Moreover, the agents in each cluster cannot communicate with agents from other clusters, except one single agent of each subnetwork, which is called a leader. These leaders interact at some instant times via fixed and strongly connected directed graph. This paper proposes a consensus protocol that takes into account the continuous-time communications among agents in the clusters and discrete information exchanges between clusters. Based on this proposed protocol, the collective network dynamics of the multi-agent systems is described in the term of hybrid systems. The characterization of the global consensus value of this kind of networks is analyzed. Secondly, we show that the problem of consensus design can be indirectly solved by considering the stability of an equivalent system. Then, a sufficient condition for the asymptotical stability of this equivalent system is proposed. Finally, an illustrative example is given to show the effectiveness of the proposed theoretical results.