Leader-following bipartite consensus of multi-agent systems under signed networks

Consensus protocols play a central role in the coordination distributed of multi-agent systems. Previous studies are mostly concentrated on the networks with only non-negative weighted edges. This paper examines the leader-following bipartite consensus problem under signed networks, where both positively and negatively weighted edges are allowed. A quantitative characterization of bipartite consensus is given according to the influence pattern of external inputs. If the agents in only one of the two clusters are influenced by external inputs, then agents in the cluster that is directly influenced by positively (resp. negatively) weighted external inputs will reach a consensus on external inputs (resp. opposite number of the external inputs), and agents in the other cluster reach a consensus on the opposite number of the external inputs (resp. external inputs). On the other hand, if agents in both clusters are influenced by external inputs with opposite signs of weights, then agents in the cluster that is directly influenced by positively (resp. negatively) weighted external input reach a consensus on external inputs (resp. opposite number of the external inputs), and agents in the other cluster will reach a consensus on the opposite number of the external inputs (resp. external inputs). Simulation results show the effectiveness of the theoretical results. © 2019, Editorial Office of Control and Decision. All right reserved.