Fixed-time bipartite consensus of multi-agent systems with disturbances

This article settles the fixed-time bipartite consensus for multi-agent systems that are subject to disturbances or not. The established protocols are aimed at controlling networked agents to reach agreement bipartitely, which reveals that a final state is the same in quantity but not in sign. By introducing algebraic graph theory, Lyapunov analysis and stability theory of fixed-time, the settling time associated with the design parameters and network connectivity rather than the initial states is explicitly given. The rationality of theoretical analysis is demonstrated via simulations.