Achieving cluster consensus in continuous-time networks of multi-agents with adapted inputs

In this paper, cluster consensus problem in continuous-time networks of multi-agents with external inputs is studied. Here, following [29], cluster consensus is defined in two aspects: intra-cluster synchronization, which means that the state differences among agents in the same cluster asymptotically converge to zero, and inter-cluster separation, which means the states of the agents in different clusters are separated. Under the inter-cluster common influence condition and with adapted inter-cluster identical inputs, the stability of cluster consensus is proved by extending the existing concepts and approaches in the matrix and graph theories to the cluster cases. The adapted inputs are also required to separate different clusters (or called inter-cluster separation). For the graph of the network, both static and switching topologies are considered. Numerical simulation to verify the theoretical results is given, too.