Leader-following consensus problem with a varying-velocity leader and time-varying delays

In this paper, we study a leader-following consensus problem for a multi-agent system with a varying-velocity leader and time-varying delays. Here, the interaction graph among the followers is switching and balanced. At first, we propose a neighbor-based rule for every agent to track a leader whose states may not be measured. In addition, we consider the convergence analysis of this multi-agent system under two different conditions: the connection between the followers and the leader is time-invariant and time-varying. For the first case, a novel decomposition method is introduced to facilitate the convergence analysis. By utilizing a Lyapunov–Krasovskii functional, we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors. Finally, two simulations are also presented to illustrate our theoretical results.