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

## TL;DR

This paper introduces a novel vector matroid-based method to analyze the structural controllability of systems over F(z), providing simpler conditions and demonstrating effectiveness through examples.

## Contribution

It develops a new matroid-theoretic framework for studying controllability over F(z), offering simpler and more intuitive conditions than existing methods.

## Key findings

- Derived full rank conditions using matroid concepts.
- Established sufficient controllability conditions for systems over F(z).
- Demonstrated the approach's simplicity through examples.

## Abstract

In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. Firstly, a vector matroid is defined over F(z). Secondly, the full rank conditions of [sI-A|B] 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.

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Source: https://tomesphere.com/paper/1704.00189