Consider the following system described by the following state space representation. \left[\begin{array}{c}˙{x\end{array}_1(t) ; ˙{x}_2(t)]}=\left[\begin{array}{cc}0 & 1 \ 0 & -2]\end{array} \left[\begin{array}{c}x_1(t) \ x_2(t)]\end{array}+\left[\begin{array}{c}0 \ 1]\end{array} u(t) y(t)=\left[\begin{array}{cc}1 & 0]\end{array}\left[\begin{array}{c}x_1(t) \ x_2(t)]\end{array} If u(t) is a unit step input and\left[\begin{array}{c}x_1(0) \ x_2(0)]\end{array}=\left[\begin{array}{c}1 \ 0]\end{array} the value of output y(t) at t = 1 sec (round off to three decimal places) is ______

GATE Electrical Engineering (EE) 2017 Shift 2 Solved Paper

Question : 56 of 65

Marks: +1, -0

Consider the following system described by the following state space representation.

{[\table ˙{x}_1(t) ; ˙{x}_2(t)]}={[\table 0 , 1 ; 0 , -2]} {[\table x_1(t) ; x_2(t)]}+{[\table 0 ; 1]} u(t)

y(t)={[\table 1 , 0]}{[\table x_1(t) ; x_2(t)]}

If u(t) is a unit step input and

{[\table x_1(0) ; x_2(0)]}={[\table 1 ; 0]}

the value of output y(t) at t = 1 sec (round off to three decimal places) is ______

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