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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 $\lim_{t\rightarrow \infty }\left | \sqrt{x_1^2(t)+x_2^2(t)} \right |$ is __________.
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