For some LTIC system $$\begin{align*} \dot{x}(t)&=Ax(t)+Bu(t)\\ x(0)&=x_{0} \end{align*}$$with control $u(t)=Fx(t)$ where $F\in M_{m\times n}$ we have that $A+BF$ is Hurwitz if and only if $A+BF$ is globally asymptotically stable i.e. $$\mathrm{Re}(eig(A+BF))<0\iff x(t)\to0\text{ as }t\to\to \infty, \ \forall x_{0}\in\mathbb{R}^{n}$$