Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays

This paper studies the consensus problems over signed digraphs with arbitrary finite communication delays. For the considered system, the information flow is directed and only locally delayed information can be used for each node. We derive that bipartite consensus of this system can be realized when the associated signed digraph is strongly connected. Furthermore, for structurally balanced networks, this paper studies the pinning partite consensus for the considered system. we design a pinning scheme to pin any one agent in the signed network, and obtain that the network achieves pinning bipartite consensus with any initial conditions. Finally, two examples are provided to demonstrate the effectiveness of our main results.