Time-varying formation control for general linear multi-agent systems with time-varying delays and switching topologies

Time-varying formation control problems for general linear multi-agent systems with switching interaction topologies and time-varying delays are investigated. Firstly, a consensus based control protocol is proposed using local neighboring information. An algorithm with three steps is presented to design the formation control protocol. Then using common Lyapunove-Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with switching topologies and time-varying delays to achieve time-varying formation are given together with a time-varying formation feasibility condition. Finally, a numerical simulation is given to demonstrate the effectiveness of the obtained theoretical results.