Necessary and sufficient conditions for containment control of networked multi-agent systems

In this paper, containment control problems for networked multi-agent systems with multiple stationary or dynamic leaders are investigated. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the achievement of containment control are established for both continuous-time and sampled-data based protocols. When the leaders are stationary, the convergence for continuous-time protocol (sampled-data based protocol) is completely dependent on the topology structure (both the topology structure and the size of sampling period). When the leaders are dynamic, the convergence for continuous-time protocol (sampled-data based protocol) is completely dependent on the topology structure and the gain parameters (the topology structure, the gain parameters, and the size of sampling period). Moreover, the final states of all the followers are exclusively determined by the initial values of the leaders and the topology structure. In the stationary leaders case, all the followers will move into the convex hull spanned by the leaders, while in the dynamic leaders case, the followers will not only move into the convex hull but also move with the leaders with the same velocity. Finally, all the theoretical results are illustrated by numerical simulations.