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In this paper, the structural controllability of leader–follower systems over digraphs is discussed. Firstly, with the aid of leader–follower partition, we analyze the topological characteristics of systems without dilations. Moreover, we divide the digraph into the leader subgraph and the follower subgraph. By analyzing the topological characteristics of the follower subgraph, a sufficient condition to ensure the system structurally controllable is given. Furthermore, some special topologies of follower graphs are analyzed, such as unidirectional cycle graphs and directed paths, and the corresponding sufficient conditions of structural controllability are given. Meanwhile, a method to construct digraphs with structural controllability is presented. Finally, the strong structural controllability of directed tree graphs is considered, as well as the selection mechanism of leaders and the lower bound of the number of leaders under strong structural controllability are given. The above results reflect the effects of topologies on strong (or weak) structural controllability. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]