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Formation-containment analysis and design problems for high-order linear time-invariant swarm systems with directed interaction topologies are dealt with respectively. 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. Secondly, formation-containment problems of swarm systems are transformed into asymptotic stability problems, and an explicit expression of the formation reference function is derived. Sufficient conditions for swarm systems to achieve formation containment are proposed. Furthermore, necessary and sufficient conditions for swarm 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. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Output containment analysis and design problems for high-order linear time-invariant swarm systems are dealt with. Firstly, output containment protocols are presented for leaders and followers, respectively, to partially assign the output motion modes of leaders and propel the outputs of followers to converge to the convex hull formed by the outputs of leaders. Then, output containment problems for swarm systems are transformed into stability problems, and sufficient conditions for swarm systems to achieve output containment are proposed. Moreover, an approach to determine the gain matrix in the protocol for swarm systems to achieve output containment is given, which has less calculation complexity. Finally, numerical simulations are presented to demonstrate theoretical results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Containment analysis and design problems for high-order linear time-invariant singular swarm systems on directed graphs with time delays are investigated. To eliminate impulse terms in singular swarm systems and ensure that the singular swarm systems can achieve containment, time-delayed protocols are presented for leaders and followers, respectively. By model transformation, containment problems of singular swarm systems are converted into stability problems of multiple low-dimensional time-delayed systems. In terms of linear matrix inequality, sufficient conditions are presented for time-delayed singular swarm systems to achieve containment, which are independent of the number of agents. By using the method of changing variables, an approach is provided to determine the gain matrices in the protocols. Numerical simulations are shown to demonstrate theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]