Formation-containment control for high-order linear time-invariant multi-agent systems

Formation-containment control problems for high-order linear time-invariant multi-agent systems with directed interaction topologies are dealt with. Firstly, protocols are presented for leaders and followers respectively to drive the states of leaders to realize the predefined time-varying formation and propel the states of followers to converge to the convex hull formed by the states of leaders. Then formation-containment problems of multi-agent systems are transformed into asymptotic stability problems and an explicit expression of the formation reference function is derived. Sufficient conditions for multi-agent systems to achieve formation-containment are proposed. Furthermore, necessary and sufficient conditions for multi-agent systems to achieve containment and time-varying formation are presented respectively as special cases. An approach to determine the gain matrices in the protocols is given. It is shown that containment problems, formation control problems, consensus problems and consensus tracking problems can all be treated as special cases of formation-containment problems. Finally, numerical simulations are provided to demonstrate theoretical results.