Bipartite consensus behavior of agents in networked systems

In this paper, bipartite consensus behavior of multiple agents in networked systems with single-integrator dynamics under directed signed graphs is investigated. It is assumed that the agents can be classified into two antagonistic groups such that the interactions between agents belonging to the same group are cooperative, while interactions between agents belonging to different groups are antagonistic. Positive weights are used to model the cooperative interactions and negative weights are used to model the antagonistic interactions. Firstly, the behavior of continuous-time agents with weighted, signed, directed graph is analyzed, including the strongly connected graph and the graph which has a spanning tree. Secondly, sampled-data based bipartite consensus of continuous-time multi-agent systems is derived. Thirdly, it is extended to the general weakly connected signed graphs. Finally, the theoretical results are illustrated by some simulations.