Cluster synchronization of coupled linear systems under directed nonnegative graphs
Zhongchang Liu, Wing Shing Wong, Hui Cheng · 2016
The cluster synchronization problem aims to understand how a multi-agent system can evolve into several clusters such that agents belonging to the same cluster get their system states synchronized. This paper studies this problem in multi-agent systems with identical generic linear dynamics. Under nonnegative assumptions for the interaction graph, this paper designs for each agent a distributed control law, and shows that cluster synchronization can be achieved if the graph topology admits directed cluster spanning trees with respect to the clustering structure. This graph topology is further proven to be a necessary condition when the clusters connect with each other without forming cycles. Numerical simulations are conducted to illustrate the theoretical results derived in this paper.