1
GATE ECE 1999
+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.
EXAM MAP
Medical
NEET