Some necessary and sufficient conditions for containment control of the second-order multi-agent systems

In this paper, distributed containment control problems of the second-order multi-agent systems under the undirected communication topology are investigated. Based on the LaSalle's Invariance Principle and the control protocols proposed in this paper, some necessary and sufficient conditions for the achievement of containment control are respectively proposed in the presence of multiple stationary leaders and multiple dynamic leaders. Finally, several simulation results are presented to support the effectiveness of our theoretical results.