On Asymptotic Stability of Leader-Follower Multi-agent Systems Under Transient Constraints

We address the agreement-based coordination of first-order multi-agent systems interconnected over arbitrary connected undirected graphs and under transient steady-state constraints. The system is in a leader-follower configuration where only part agents, leaders, are directly controlled via an external control input, addition to agreement protocol. propose law for based on gradient potential function, that achieves consensus guarantees trajectories inter-agent distances entire remain bounded by performance function. Relying edge-agreement framework Lyapunov’s first method, we establish strong stability results sense asymptotic manifold and, leaderless case, nonuniform-in-time input-to-state with respect additive disturbances. A numerical simulation illustrates effectiveness proposed approach.