1
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
Given A $$ = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the state transition matrix eAt is given by
A
$$\left[ {\matrix{ 0 & {{e^{ - t}}} \cr {{0^{ - t}}} & 0 \cr } } \right]$$
B
$$\left[ {\matrix{ {{e^t}} & 0 \cr 0 & {{e^t}} \cr } } \right]$$
C
$$\left[ {\matrix{ {{e^{ - t}}} & 0 \cr 0 & {{e^{ - t}}} \cr } } \right]$$
D
$$\left[ {\matrix{ 0 & {{e^t}} \cr {{e^t}} & 0 \cr } } \right]$$
2
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
The state variable equations of a system are: $$${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u$$$ $$${\mathop x\limits^ \bullet _2} = 2{x_1}$$$ $$$y = {x_1} + u.$$$
The system is
A
controllable but not observable.
B
observable but not controllable.
C
neither controllable nor observable.
D
controllable and observable.
3
GATE ECE 2003
MCQ (Single Correct Answer)
+2
-0.6
The zero, input response of a system given by the state space equation $$$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \over {\mathop {{x_2}}\limits^ \bullet }}} \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]and\left[ {\matrix{ {{x_1}} & {\left( 0 \right)} \cr {{x_2}} & {\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr } } \right]is$$$
A
$$\left[ {\matrix{ {t{e^t}} \cr t \cr } } \right]$$
B
$$\left[ {\matrix{ {{e^t}} \cr t \cr } } \right]$$
C
$$\left[ {\matrix{ {{e^t}} \cr {t{e^t}} \cr } } \right]$$
D
$$\left[ {\matrix{ t \cr {t{e^t}} \cr } } \right]$$
4
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
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