Cluster Consensus of Multiagent Systems With Weighted Antagonistic Interactions

This article addresses the problem of cluster consensus for multiagent systems (MASs) associated with weighted antagonistic interactions. Compared with some existing results, a general communication topology among agents is introduced in this article, where there is no need to confine directed cycles to the root of a spanning tree. By taking into consideration the structures of directed cycles and multiple paths, the judgment of structural balance is simplified significantly. A novel cluster consensus protocol is also proposed for structurally unbalanced digraphs. Moreover, two necessary and sufficient conditions are derived, by which cluster consensus can be achieved in an MAS if and only if its communication topology contains a directed spanning tree. Then, by employing an algebra theorem, a sufficient criterion for the unstable system under a directed cycle is obtained, whether the number of agents on this cycle is odd or even. Some illustrative examples are given to demonstrate the effectiveness of theoretical results.