State variable description of an LTI system is given by \left[\begin{array}{c}˙{x\end{array}_1 ; ˙{x}_2 ; ˙{x}_3]}=\left[\begin{array}{ccc}0 & a_1 & 0 \ 0 & 0 & a_2 \ a_3 & 0 & 0]\end{array}\left[\begin{array}{c}x_1 \ x_3 \ x_3]\end{array}+\left[\begin{array}{c}0 \ 0 \ 1]\end{array} U Y=\left[\begin{array}{ccc}1 & 0 & 0]\end{array}\left[\begin{array}{c}x_1 \ x_2 \ x_3]\end{array} Where Y is the output and u is input. System is controllable for

Correct Answer is : a1 ≠ 0, a2 ≠ 0, a3 = 0

GATE Electronics and Communications (EC) 2012 Solved Paper

Question : 42 of 65

Marks: +1, -0

State variable description of an LTI system is given by

{[\table ˙{x}_1 ; ˙{x}_2 ; ˙{x}_3]}={[\table 0 , a_1 , 0 ; 0 , 0 , a_2 ; a_3 , 0 , 0]}{[\table x_1 ; x_3 ; x_3]}+{[\table 0 ; 0 ; 1]} U

Y={[\table 1 , 0 , 0]}{[\table x_1 ; x_2 ; x_3]}

Where Y is the output and u is input. System is controllable for

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