We define an affine control system as $$\dot{x}=f(x)+g(x)u$$with $x\in \mathbb{X}\subset \mathbb{R}^{n},u\in \mathbb{U}\subset \mathbb{R}^{q}$, where $\mathbb{U}$ is closed and $f:\mathbb{R}^{n}\to \mathbb{R}^{n},g:\mathbb{R}^{n}\to \mathbb{R}^{n\times q}$ locally Lipschitz.