Containment control of multi-agent systems with nonuniform time-delays under fixed topology

This paper studies the containment control issue of continuous-time multi-agent systems (MASs) with nonuniform time-delays and stationary/dynamic leaders, respectively. Firstly, by the state transformation method, the containment control problem can be converted into the asymptotic stability of the corresponding ordinary differential equations. Then, for single-order MASs with stationary leaders, containment control can be achieved if for each follower, there exists at least a leader which has a directed path to the follower. Moreover, our results show that arbitrary bounded time delays can be tolerated. On the other hand, for second-order MASs with dynamic leaders, by Lyapunov first method, we mainly provide the upper bound tau* of time delays such that MASs can achieve the containment control in an exponential convergence rate. Finally, experimental results are provided to illustrate the effectiveness of the theoretical results.