On Asymptotic Stability of Leader–Follower Multiagent Systems Under Transient Constraints

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