Consider an LTIC system $$\begin{align*} \dot{x}(t)&=Ax(t)+Bu(t)\\ x(0)&=x_{0} \end{align*}$$where the input is chosen to be $u(t)=Fx(t)$, where $F$ is $m\times n$ then $$\begin{align*} \dot{x}(t)&=(A+BF)x(t)\\ x(0)&=x_{0} \end{align*}$$The solution to this is given by $$x(t)=e^{(A+BF)t}x_{0}\quad t\ge0$$We wish to know when it is possible to choose $F$ s.t. $A+BF$ is Hurwitz. We see if $A+BF$ is Hurwitz then $x(t)\to 0$ as $t\to \infty$ $\forall x_{0}\in\mathbb{R}^{n}$.