Stationary containment control of high-order multi-agent systems with time-varying delays

This paper addresses the containment control problem for discrete-time high-order multi-agent systems with time-varying delays. Based on the distributed containment control protocol only depends on the agent's own information and its neighbors' partial information, the properties of the product of infinite nonnegative matrices and the composite of binary relation are utilized to derive a necessary and sufficient condition that the containment control of high-order multi-agent systems can be achieved if and only if the directed communication topology contains a spanning forest. Finally, some numerical simulations are presented to illustrate the effectiveness of our theoretical results.