Definition (Stabilizable)

Let $A\in M_{n}(\mathbb{R}),B\in M_{n\times m}(\mathbb{R})$. Then $(A,B)$ is called stabilizable if $\tilde{A}_{22}$ in its Controllability Normal Form is Hurwitz or $\tilde{A}_{22}$ does not exist (i.e. $(A,B)$ is Controllable).