Summary In this paper, the controllability of multi‐agent systems is studied under leader‐follower framework, where the interconnection between agents is directed. The concept of leader‐follower connectedness is first introduced for directed graph to check controllability, and some graph‐theoretic conditions are derived for constructively designed topologies. Then, distance partition and almost equitable partition are employed to quantitatively study the controllable subspaces. Moreover, the relationship between the state invariance of multi‐agent systems and the existence of almost equitable partition is discussed. Copyright © 2017 John Wiley & Sons, Ltd.

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