Bipartite Consensus Analysis on Clustered Signed Networks of Multi-Agent with Reset Control

This paper investigates the bipartite consensus problem of multi-agent systems (MASs) on the clustered and signed networks with reset control. We divide the agents into several subclusters which are in two camps with interactions within and outside the subclusters represented by different topologies. Through constructing a non-negative connected digraph with directed spanning trees in each subcluster, the agents within the subcluster can achieve local consensus by interacting in continuous time. Meanwhile, a signed graph of structural balance is used to indicate the relationships between subclusters are cooperative or antagonistic. Our main contribution is to propose a bipartite consensus protocol for interaction between subcluster leaders at discrete moments. The bipartite consensus formula and the Linear Matrix Inequality (LMI) condition are analyzed by using the gauge transformation. The results show that the bipartite consensus value is affected by the initial state of the agents, the interaction topology of intra-subcluster and the signed graph of inter-subcluster. Finally, two numerical examples are provided to verify the correctness of the bipartite consensus protocol.