Cluster Consensus Control of Linear Multiagent Systems Under Directed Topology With General Partition

This article investigates the cluster consensus control problem for general linear multiagent systems. The focus of this article is especially to solve the following problem: in what kinds of connection scenarios can agents achieve cluster consensus regardless of the coupling strength (CCRCS). Different from existing literature, this article extends the case to general partition graphs, including both acyclic and cyclic partition cases. New analysis methods are put forward. It is proved that, under some basic assumptions, the multiagent systems can achieve CCRCS if and only if the interaction topology satisfies the nonvicious circle condition, which is proposed for the first time. An algorithm is presented which can check whether a given interaction topology satisfies the nonvicious circle condition. The result can also be extended to heterogeneous cases that agents from different clusters possess nonidentical system dynamics.