Distributed PD-type protocol based containment control of multi-agent systems with input delays

In this paper, we investigate the containment control problem with directed communication topologies and time delays. Compared with the widely used containment controller, a distributed PD-type protocol based on the information of neighbors considering the effects of input delays is adopted. A parameter condition for the containment control problem is provided; it is shown that under this condition, the states of the followers will asymptotically converge to the convex hull spanned by the states of leaders if the graph has a directed spanning forest. Then, based on the provided parameter condition, the maximal upper bound of the input delays is obtained by using the pole analysis method. Finally, the numerical examples are used to illustrate the theoretical results.