Robust H∞H∞ containment control for second-order multi-agent systems with nonlinear dynamics in directed networks

This paper considers robust H∞H∞ containment control problem in directed networks for second-order multi-agent systems with inherent nonlinear dynamics. A distributed control protocol is proposed for each follower using the relative states among neighboring agents. The original problem under the proposed protocol is then converted into an H∞H∞ control problem by defining an appropriate controlled output function. Based on robust H∞H∞ control approach, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H∞H∞ performance. Finally, a numerical example is provided to demonstrate the effectiveness of our theoretical results.