Fixed-Time Consensus for Cooperative and Antagonistic Multi-Agent Systems With External Disturbances and Directed Topologies

The aim of this paper is to investigate the fixed-time consensus problems of cooperative and antagonistic multi-agent systems (CAMSs) with both antagonistic interactions and external disturbances under directed topologies. Toward this end, a nonlinear control protocol is constructed according to the nearest neighbor information. With the aid of the properties of improved Laplacian potentials, the associated convergence analyses can be developed from the viewpoint of Lyapunov stability theory. It is shown that all the agents can accomplish the bipartite consensus (respectively, state stability) objective within a fixed time under structurally balanced (respectively, unbalanced) signed digraphs in spite of the existing external disturbances. Additionally, simulations are included to validate the developed results.