Observer-based containment control of multi-agent system with linear dynamics

This paper considers the containment control of linear multi-agent system with weakly connected information topology. By defining the node-induced strongly connected subgraph as strong component, the agents contained in strong components with zero in-degree are called leaders and the others are called followers. Then, a sufficient and necessary condition is proposed for all agents to achieve containment by employing an observer-based protocol, where all followers finally converge to the convex hull formed by leaders and each strong component of leaders asymptotically achieve consensus. Since the number of leader agents in each strong component are always larger than one, the proposed scheme is more robust for the malfunction of leaders. Further, two LMIs are given to design the observer-based protocol. Numerical examples are included to illustrate the validity of the proposed results.