The transfer function of the system \frac{Y (s) }{U (s) } whose state-space equations are given below is: \left[\begin{array}{c}˙{x\end{array}_1(t) ; ˙{x}_2(t)]}=\left[\begin{array}{cc}1 & 2 \ 2 & 0]\end{array} \left[\begin{array}{c}x_1(t) \ x_2(t)]\end{array}+\left[\begin{array}{c}1 \ 2]\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}

Correct Answer is : (s+4)(s2−s−4)

\frac{ (s + 2) }{ (s^{2}−2s−2) }

\frac{ (s−2) }{ (s^{2} + s−4) }

\frac{ (s−4) }{ (s^{2} + s−4) }

\frac{ (s + 4) }{ (s^{2}−s−4) }

GATE Electrical Engineering (EE) 2017 Shift 1 Solved Paper

Question : 43 of 65

Marks: +1, -0

The transfer function of the system

\;{Y\;(s)\;}/{U\;(s)\;}

whose state-space equations are given below is:

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

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

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