1
GATE ECE 2015 Set 3
MCQ (Single Correct Answer)
+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
$${{11s - 38} \over {\left( {s - 2} \right)\left( {s + 4} \right)}}$$
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 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
$$\left[ {\matrix{ 1 & t \cr 0 & 1 \cr } } \right]$$
4
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = {x_0}.$$
For $${x_0} = \left[ {\matrix{ 1 \cr { - 1} \cr } } \right],x\left( t \right) = \left[ {\matrix{ {{e^{ - t}}} \cr { - {e^{ - t}}} \cr } } \right]$$ and for $${x_0} = \left[ {\matrix{ 0 \cr 1 \cr } } \right],x\left( t \right) = \left[ {\matrix{ {{e^{ - t}}} & { - {e^{ - 2t}}} \cr { - {e^{ - t}}} & { + 2{e^{ - 2t}}} \cr } } \right]$$ when $${x_0} = \left[ {\matrix{ 3 \cr 5 \cr } } \right],x\left( t \right)$$ is
A
$$\left[ {\matrix{ { - 8{e^{ - t}}} & { + 11{e^{ - 2t}}} \cr {8{e^{ - t}}} & { - 22{e^{ - 2t}}} \cr } } \right]$$
B
$$\left[ {\matrix{ {11{e^{ - t}}} & { - 8{e^{ - 2t}}} \cr { - 11{e^{ - t}}} & { + 16{e^{ - 2t}}} \cr } } \right]$$
C
$$\left[ {\matrix{ {3{e^{ - t}}} & { - 5{e^{ - 2t}}} \cr { - 3{e^{ - t}}} & { + 10{e^{ - 2t}}} \cr } } \right]$$
D
$$\left[ {\matrix{ {5{e^{ - t}}} & { - 3{e^{ - 2t}}} \cr { - 5{e^{ - t}}} & { + 6{e^{ - 2t}}} \cr } } \right]$$
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