Strong Structural Controllability Based on Leader-Follower Framework

In this paper, the strong structural controllability of the leader-follower framework is discussed. Firstly, the authors analyze different edge augmentation methods to preserve the strong structural controllability of the path-bud topology. The following four cases are considered: Adding edges from the path to the bud; adding edges from the bud to the path; adding the reverse or forward edges to the path or bud; and adding both the reverse and forward edges to the path or bud. Then sufficient conditions are derived for the strong structural controllability of the new topologies which are generated by adding different edges. In addition, it is proved that rank[A B] = n is a necessary condition for the strong structural controllability. Finally, three examples are given to verify the effectiveness of the main results.