Necessary and sufficient conditions for distributed containment control of multi-agent systems without velocity measurement

This study investigates the distributed containment control for second-order multi-agent systems with multiple stationary or dynamic leaders based on only position information. Based on stability and algebraic graph theories, some necessary and sufficient conditions are obtained. Firstly, when the leaders are stationary, a necessary and sufficient condition is given to guarantee that all followers will ultimately converge to the stationary convex hull spanned by the stationary leaders for arbitrary initial states. The containment control protocol is designed based on a distributed filter, which is used for estimating the neighbours´ velocities of each follower. Secondly, when each leader is dynamic with constant velocity, using sampled current and outdated position data, a necessary and sufficient condition is obtained to drive the followers into the dynamic convex hull spanned by the dynamic leaders. Finally, some numerical simulations are presented to illustrate the proposed theories.