Consider the state space realization \left[\begin{array}{c}˙{x\end{array}_1(t) ; ˙{x}_2(t)] =\left[\begin{array}{cc}0 & 0\ 0 & -9]\end{array} [ \table x_1(t) ; x_2(t)]+\left[\begin{array}{c}0 \ 45]\end{array} u(t) with the initial condition \left[\begin{array}{c}x_1(0) \ x_2(0)]\end{array}=\left[\begin{array}{c}0 \ 0]\end{array}. where u(t) denotes the unit step function. The value of {\lim}_{t\to \infty}⁡ |\sqrt{x_{1}^{2} (t) + x_{2}^{2} (t) }{{}/{}|} is ________.

GATE Electronics and Communications (EC) 2017 Shift 2 Solved Paper

Question : 29 of 65

Marks: +1, -0

Consider the state space realization

{[\table ˙{x}_1(t) ; ˙{x}_2(t)] ={[\table 0, 0; 0, -9]} [ \table x_1(t) ; x_2(t)]+{[\table 0 ; 45]} u(t)

with the initial condition

{[\table x_1(0) ; x_2(0)]}={[\table 0 ; 0]}

.
where u(t) denotes the unit step function. The value of

{\lim}↙{t→ ∞}⁡ |√{x_{1}^{2} (t) + x_{2}^{2} (t) }{{}/{}|}

is ________.

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