Finite‐time and fixed‐time bipartite consensus of nonlinear multi‐agent systems with perturbations and input delays

This paper investigates the finite‐time and fixed‐time bipartite consensus problem in nonlinear multi‐agent systems with perturbations and input delays, operating within an undirected structured equilibrium topology graph. By leveraging the competitive and cooperative dynamics inherent in multi‐agent systems, we develop distributed control protocols to achieve finite‐time and fixed‐time bipartite consensus through a model downgrading approach. Through rigorous theoretical analysis of these consensus control protocols, we employ Lyapunov's finite‐time and fixed‐time stability theory in conjunction with algebraic graph theory to demonstrate that multi‐agent systems can achieve both finite‐time and fixed‐time bipartite consensus despite perturbations and input delays. We establish sufficient conditions for system convergence by applying Lyapunov's fixed‐time stability theory integrated with algebraic graph theory, thereby validating the efficacy of our distributed control protocol. The feasibility and effectiveness of both the distributed control protocol and our theoretical findings are subsequently confirmed through comprehensive simulation studies.