Predefined formation-containment control of high-order multi-agent systems under communication delays and switching topologies

This paper concerns the problem of formation-containment control for general-linear multi-agent systems (MASs) with both communication delays and switching interaction topologies. On the one hand, the leaders can communicate with each other to form the desired formation and on the other, the followers need to enter the convex envelope spanned by the multiple leaders. Firstly, by using the neighbouring relative information, formation-containment protocols are designed for each leader and follower, where an edge-based state observer is incorporated into the formation-containment controller to evaluate the whole leaders' state. Secondly, according to the linear matrix inequality technology, an algorithm is given to determine the unknown feedback matrixes in the protocol. Then, based on Lyapunov theory, the formation-containment error is proved to be convergent and formation feasibility conditions are also presented for the MASs to achieve formation-containment. Finally, a simulation on several MASs is provided to demonstrate the theoretical results.