Fixed-time leader-follower bipartite consensus of nonlinear multi-agent systems with a leader of nonzero input

This study investigates the fixed-time bipartite consensus (FTBC) problem for leader-follower nonlinear multi-agent systems (MASs) with nonzero control input for leader and external disturbances. The cooperative-antagonistic relationships between agents are characterized by a structurally balanced signed graph. First, a generalized Lipschitz-type condition is introduced to realize the bipartite consensus of the MASs. A distributed fixed-time controller was then designed to guarantee the FTBC. The upper bound of the convergence time and the sufficient condition for the realization of the FTBC are obtained by applying graph theory and Lyapunov theory. Finally, the effectiveness of the control algorithm is verified through numerical simulations.