In this technical note, cluster consensus in continuous-time networks of multi-agents with time-varying topologies via non-identical inter-cluster inputs is studied. The cluster consensus contains two aspects: intra-cluster synchronization, that the state differences between agents in the same cluster converge to zero, and inter-cluster separation, that the states of the agents in different clusters do not approach. δ-cluster-spanning-tree in continuous-time networks of multi-agent systems plays essential role in analysis of cluster synchronization. Inter-cluster separation can be realized by imposing adaptive inputs that are identical within the same cluster but different in different clusters, under the inter-cluster common influence condition. Simulation examples demonstrate the effectiveness of the derived theoretical results.
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Han et al. (2014) studied this question.
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