1
GATE ECE 1999
MCQ (Single Correct Answer)
+2
-0.6
For the system described by the state equation $$$\mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr {0.5} & 1 & 2 \cr } } \right]x + \left[ {\matrix{ 0 \cr 0 \cr 1 \cr } } \right]u.$$$


If the control signal u is given by u=(-0.5-3-5)x+v, then the eigen values of the closed loop system will be

A
0, -1, -2
B
0, -1, -3
C
-1, -1, -2
D
0, -1, -1
2
GATE ECE 1997
MCQ (Single Correct Answer)
+2
-0.6
A certain linear time invariant system has the state and the output equations given below $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & { - 1} \cr 0 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 0 \cr 1 \cr } } \right]u$$$ $$$y = \left[ {\matrix{ 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right], if$$$ $${x_1}\left( 0 \right) =1 ,{x_2}\left( 0 \right) = - 1,$$ $$u\left( 0 \right) = 0,$$ then $${{dy} \over {dt}}{|_{t = 0}}$$ is
A
1
B
-1
C
0
D
None of the above
3
GATE ECE 1992
MCQ (More than One Correct Answer)
+2
-0.6
A linear time-invariant system is described by the state variable model $$$\left[ {\matrix{ {{{\mathop x\limits^ \bullet }_1}} \cr {{{\mathop x\limits^ \bullet }_2}} \cr } } \right] = \left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 0 \cr 1 \cr } } \right]u.$$$ $$$Y = \left[ {\matrix{ 1 & 2 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$$
A
The system is completely controllable
B
The system is not completely controllable
C
The system is completely observable
D
The system is not completely observable
4
GATE ECE 1991
MCQ (Single Correct Answer)
+2
-0.6
A linear second order single input continuous-time system is described by the following set of differential equations $$$\eqalign{ & \mathop {{x_1}}\limits^ \bullet \left( t \right) = - 2{x_1}\left( t \right) + 4{x_2}\left( t \right) \cr & \mathop {{x_1}}\limits^ \bullet \left( t \right) = 2{x_1}\left( t \right) - {x_2}\left( t \right) + u\left( t \right) \cr} $$$
Where x1(t) and x2(t) are the state variables and u (t) is the control variable. The system is
A
controllable and stable.
B
controllable but unstable.
C
uncontrollable and unstable.
D
uncontrollable but stable.
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