Consider the state space realization

$\begin{bmatrix} \dot{x_1}(t)\\ \dot{x_2}(t) \end{bmatrix}=\begin{bmatrix} 0 &0 \\ 0&-9 \end{bmatrix}\begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}+\begin{bmatrix} 0\\ 45 \end{bmatrix} u(t)$ , with the initial condition $\begin{bmatrix} x_1(0)\\ x_2(0) \end{bmatrix}=\begin{bmatrix} 0\\ 0 \end{bmatrix}$ ,

where $u(t)$ denotes the unit step function. The value of $\underset{t\rightarrow \infty }{\lim}\left | \sqrt{x_1^2(t)+x_2^2(t)} \right |$ is __________.