Pinning Control for Asymmetric Bipartite Consensus of Antagonistic Multi-agent Networks with Delays

This note investigates the pinning asymmetric bipartite consensus for multi-agent networks with antagonistic interactions and communication delays. A pinning asymmetric bipartite consensus protocol is designed firstly for the considered delayed multi-agent systems. It is shown that, under the proposed consensus protocol, the pinning asymmetric bipartite consensus can be realized if the addressed signed digraph is strongly connected and structurally balanced. Furthermore, for the signed digraph with spanning trees, we subtly design a pinning interval asymmetric bipartite consensus protocol to make all the agents converge within a predetermined interval. Finally, two examples are given to demonstrate effectiveness of our theoretical results.