This paper investigates the affection of automorphism on controllability for the multi-agent systems with leader-follower framework. By using graph theory and matrix theory, we obtain a criterion for determining the existence of automorphism structure of multi-agent systems. Based on the analyzing of automorphism, we point out the relationship between automorphism and controllability of, which provides a method on the aspect of graphics to identify judging the controllability. In addition, this paper also extends the single leader symmetric systems to the multi-leader symmetric systems, which investigates the controllability of leader selection, and provides the directions and methods for further researches on the controllability of complex topological structures
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