Containment control for high-order multi-agent systems with heterogeneous time delays

This study addresses the containment control problem for high-order multi-agent systems with heterogeneous time delays. Here the authors consider two cases: the leaders are stationary and the leaders are dynamic. Based on the distributed containment control protocols with proper gain parameters, they utilise the properties of the product of infinite matrices to derive some sufficient conditions. The obtained results guarantee that all the followers can asymptotically converge to a convex hull spanned by those of the leaders under the proper gain parameters if the communication topology contains a directed spanning forest rooted at the leaders. Finally, some numerical simulations are presented to illustrate the effectiveness of their theoretical results.