Containment control of multi-agent systems with time delay

This paper studies the containment control issue of multi-agent systems with time delay. By adopting continuous-time and sampled-data-based control protocols, we establish some necessary and sufficient containment control criteria for multi-agent systems with time delay. For the continuous-time case, our results show that both topology structure and time delay play an important role in the containment control of multi-agent systems, no matter whether the leaders are stationary (first-order system) or dynamic with constant velocity and time-varying position (second-order system). Furthermore, the maximum value of time delay to guarantee the achievement of containment control is given by the Hopf bifurcation theory. Moreover, we extend the results to the sampled-data case. Finally, numerical simulations are given to illustrate our main results.