Containment of linear multi-agent systems under general interaction topologies

In this paper, the behavior of multiple agents with linear dynamics is investigated by the study of interaction topologies. According to the topology structure, the agents are classified into two categories: internal agents and boundary agents. The containment control problem proposed in this paper is that the boundary agents in the same strong component achieve consensus asymptotically, and all the internal agents converge to the convex hull spanned by the boundary agents. Furthermore, by introducing a leader into the multi-agent team, a pinning control strategy is designed for a part of agents such that all the agents can reach a consensus with the leader asymptotically. It is also shown that how to select agents with which the leader communicates such that consensus can be reached and the number of selected agents is minimum. All the results are illustrated by some simulations.