Necessary and sufficient conditions for multi-agent controllability of path and star topologies by exploring the information of second-order neighbours
Chao Yongcui, Zhijian Ji · IMA Journal of Mathematical Control and Information · 2016
Abstract This article investigates the controllability of path and star graphs under the protocol of second-order neighbours. With identified special control nodes, a sufficient condition is first derived for the controllability of path graph by taking advantage of the protocol of second-order neighbours. Then necessary and sufficient conditions are developed respectively for the single and multiple leaders. Some differences between the protocol of second-order neighbours and first-order neighbours are also presented for path graph. Finally, a necessary and sufficient condition is proposed for the controllability of star graph by taking advantage of the protocol of second-order neighbours.