In this paper, the structural controllability of the systems over F(z) is studied using a new
mathematical method-matroids. First, a vector matroid is de ned over F(z). Second, the full rank conditions
of [sI AB](s 2 ) are derived in terms of the concept related to matroid theory, such as rank, base, and
union. Then, the suf cient condition for the linear system and composite system over F(z) to be structurally
controllable is obtained. Finally, this paper gives several examples to demonstrate that the married-theoretic
approach is simpler than other existing approaches.