Delay Margin for Containment Control of Second-Order Multi-Agent Systems over Directed Graphs

In this paper, we mainly study the delay robustness on containment control of second-order multi-agent systems with uncertain communication delays over directed graphs. Our purpose is to find the maximal delay range that can be tolerated under which the multi-agent system can maintain containment robustly. We consider a second-order multi-agent system under position and velocity feedback protocols in which each agent has two unstable real poles. We derive the exact expression of the delay margin for multi-agent system containment. Furthermore, based on the analysis of the exact delay margin, we obtain its explicit upper bound. The results show that the position of poles and the network connectivity will affect the bound of delay margin. Finally, a numerical example is used to illustrate the effectiveness of the proposed theoretical results.