Formation-containment control for general linear multi-agent systems with time-varying delays and switching topologies

Formation-containment control problems for general linear multi-agent systems with time-varying delays and switching topologies are studied. The leaders are required to accomplish a given time-varying formation and the followers are allowed to enter the convex envelope spanned by those of the leaders simultaneously. Firstly, formation-containment protocols based on distributed state observer with switching interaction topologies and time-varying delays are presented for leaders and followers respectively, where an edge-based state observer is presented for each follower to estimate the whole states of all the leaders under the influences of switching interaction topologies and time-varying delays. Then, formation-containment problems are transformed into asymptotic stability problems. Furthermore, an algorithm to determine the gain matrices in the protocols is given based on linear matrix inequality technique and common Lyapunov-Krasovskii stability theory. Sufficient conditions for multi-agent systems to achieve formation-containment under the designed protocol are proposed. Finally, numerical simulations are provided to demonstrate theoretical results.