Formation-containment control of sampled-data second-order multi-agent systems with sampling delay

The formation-containment control problems of sampled-data second-order multi-agent systems with sampling delay are studied. In this paper, we assume that there exist interactions among leaders and that the leader’s neighbours are only leaders. Firstly, two different control protocols with sampling delay are presented for followers and leaders, respectively. Then, by utilizing the algebraic graph theory and matrix theory, several sufficient conditions are obtained to ensure that the leaders achieve a desired formation and that the states of the followers converge to the convex hull formed by the states of the leaders, i.e. the multi-agent systems achieve formation containment. Furthermore, an explicit expression of the formation position function is derived for each leader. An algorithm is provided to design the gain parameters in the protocols. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.