1
GATE ECE 2016 Set 3
+2
-0.6
A second-order linear time-invariant system is described by the following state equations \eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \right) \cr & {d \over {dt}}{x_2}\left( t \right) + {x_2}\left( t \right) = u\left( t \right) \cr}Where x1(t), then the system is A controllable but not observable B observable but not controllable C both controllable and observable D neither controllable nor observable 2 GATE ECE 2015 Set 2 MCQ (Single Correct Answer) +2 -0.6 The state variable representation of a system is given as \eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 & { - 1} \cr } } \right]x;x\left( 0 \right) = \left[ {\matrix{ 1 \cr 0 \cr } } \right] \cr & y = \left[ {\matrix{ 0 & 1 \cr } } \right]x \cr}

The response y(t) is

A
sin(t)
B
1-et
C
1-cos(t)
D
0
3
GATE ECE 2015 Set 3
+2
-0.6
A network is described by the state model as \eqalign{ & {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u, \cr & \mathop {{x_2}}\limits^ \bullet = - 4{x_2} - u, \cr & y = 3{x_1} - 2{x_2} \cr}$the transfer function H(s)$$\left[ { = {{Y\left( s \right)} \over {U\left( s \right)}}} \right]is$$ A $${{11s + 35} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$ B $${{11s - 35} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$ C $${{11s + 38} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$ D $${{11s - 38} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$ 4 GATE ECE 2014 Set 4 MCQ (Single Correct Answer) +2 -0.6 The state transition matrix $$\phi \left( t \right)$$ of a system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr 0 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] is$$$
A
$$\left[ {\matrix{ t & 1 \cr 1 & 0 \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & 0 \cr t & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ 0 & 1 \cr 1 & t \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & t \cr 0 & 1 \cr } } \right]$$
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