Cluster synchronization of a class of multi-agent systems with a bipartite graph topology

This paper investigates cluster synchronization of a class of multi-agent systems with a directed bipartite graph topology,and presents a number of new results by using the neighbor’s rules for the following two cases:I)there is competition among the agents of diferent clusters,and II)there are both competition and cooperation among the agents.Firstly,for case I),a linear control protocol is designed for cluster synchronization of multi-agent systems,and a method is presented to determine the final state with the initial conditions based on state-space decomposition.Secondly,we study case II),and design a control protocol based on the information of neighbors and that of two-hop neighbors(that is,neighbors’neighbors).Finally,two examples are studied by using our presented results.The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the cluster synchronization of this class of multi-agent systems.