Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders

This paper considers the containment control problems for both continuous-time and discrete-time multi-agent systems with general linear dynamics under directed communication topologies. Distributed dynamic containment controllers based on the relative outputs of neighboring agents are constructed for both continuous-time and discrete-time cases, under which the states of the followers will asymptotically converge to the convex hull formed by those of the leaders if, for each follower, there exists at least one leader that has a directed path to that follower. Sufficient conditions on the existence of these dynamic controllers are given. Static containment controllers relying on the relative states of neighboring agents are also discussed as special cases.