Fixed-time bipartite consensus of delayed nonlinear multi-agent systems under antagonistic network

In this paper, the fixed-time bipartite consensus problem is investigated for a class of nonlinear multi-agent systems with input delay under an undirected signed graph, and the signed graph is structurally balanced. Firstly, a fixed-time distributed consensus control protocol of multi-agent systems with input delay is designed for the cooperation and competition behaviors among agents, which guarantees the system states converge to two same values but opposite signs in a fixed time, and the upper bound of convergence time is independent of the initial states. Then, the sufficient conditions are proposed for the multi-agent systems to achieve the fixed-time bipartite consensus with input delay by using the Lyapunov stability theory and algebraic graph theory, and the stability of the control algorithm is proved. Meanwhile, the upper bound of convergence time is given. Finally, the effectiveness of the proposed fixed-time bipartite consensus algorithm and the theoretical analysis results are illustrated by the simulation examples. © 2023 South China University of Technology. All rights reserved.