1
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
2
GATE ECE 1991
+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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