H∞ containment control for second-order multi-agent systems with time delay

This paper is devoted to a containment control problem with time-delay for second-order nonlinear multi-agent systems subject to external disturbances under a directed communication topology. First of all, a distributed delay-coupled protocol is proposed based on relative states among the neighboring agents. Then, sufficient conditions in terms of linear matrix inequality(LMI) are derived to make the followers asymptotically converge to the convex hull spanned by the leaders while satisfying desired H_∞ performance. It is proved that the time-delay protocol is sensitive to time delays. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.