Output formation-containment control for high-order swarm systems with directed topologies

Output formation-containment analysis problems for swarm systems with high-order linear dynamics and directed topologies are dealt with. Output formation-containment means that outputs of leaders achieve the predefined formation, and at the same time the outputs of followers can be expressed as the convex combination of outputs of leaders. Firstly, static output formation-containment protocols are constructed for leaders and followers. Then output formation containment analysis problems for swarm systems with high-order dynamics are converted into stability problems and an explicit description of the time-varying output formation reference function is obtained. Sufficient conditions for swarm systems with high-order dynamics to achieve output formation-containment are proposed. An approach to decrease the calculation complexity of the criteria is presented. Finally, a numerical simulation is provided to validate the theoretical results.