A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z)

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 defined over $F$ ( $z$ ). Second, the full rank conditions of $[sI-A\vert B](s\in \wp )$ are derived in terms of the concept related to matroid theory, such as rank, base, and union. Then, the sufficient 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.