Bipartite Consensus Problems of Directed Cooperative and Antagonistic Networks with Communication Time‐Varying Delays

Abstract

This paper concerns the bipartite consensus problems of directed cooperative and antagonistic networks (CANs) with time‐varying communication delays. A distributed control protocol is proposed based on the nearest neighbor rule. In order to derive the convergence analysis of the proposed protocol, a model transformation is introduced, based on which the consensus can be equivalently transformed into the asymptotic stability of a reduced‐order system. Besides, the sufficient conditions are provided to ensure the bipartite consensus (respectively, state stability) of CANs whose topologies are structurally balanced (respectively, unbalanced). In addition, numerical examples are given to illustrate the effectiveness of our developed results. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.