Consider the state space realization
\(\left[ {\begin{array}{*{20}{c}} {{{\dot x}_1}\left( t \right)}\\ {{{\dot x}_2}\left( t \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0&0\\ 0&{ - 9} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_1}\left( t \right)}\\ {{x_2}\left( t \right)} \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0\\ {45} \end{array}} \right]u\left( t \right),\) with the initial condition \(\left[ {\begin{array}{*{20}{c}} {{x_1}\left( 0 \right)}\\ {{x_2}\left( 0 \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0\\ 0 \end{array}} \right].\)
where u(t) denotes the unit step function. The value of
\(\mathop {\lim }\limits_{t \to \infty } \left| {\sqrt {x_1^2\left( t \right) + x_2^2\left( t \right)} } \right|\) is ________.
Enter numerical value using the virtual keypad. Round off where necessary.