Leader-following bipartite consensus of high-order multi-agent systems on signed networks

This paper investigates the bipartite consensus for a group of agents with a leader. The interaction topology among agents is directed, weighted, signed and structurally balanced. Some sufficient and necessary conditions are derived for the bipartite consensus of the leader-following multi-agent system. Specifically, under the assumption that the interaction graph involving the leader has a spanning tree, the leader-following bipartite consensus can be achieved if and only if the dynamics of the agents is stabilizable. Furthermore, an LMI-based method is proposed for the design of control gain. The results are illustrated via examples.