1
GATE EE 2002
+1
-0.3
The state transition matrix for the system $$\mathop X\limits^ \bullet = AX\,\,$$ with initial state $$X(0)$$ is
A
$${\left( {s{\rm I} - A} \right)^{ - 1}}$$
B
$${e^{AT}}\,X\left( 0 \right)$$
C
Laplace inverse of $$\,\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}} \right]$$
D
Laplace inverse of $$\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}X\left( 0 \right)} \right]$$
2
GATE EE 2001
+1
-0.3
Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\, = \mathop {Lim}\limits_{t \to \infty } x\left( t \right),$$ given the initial state value of $$x\left( 0 \right) = {\left[ {10 - 10} \right]^T},\,\,is$$
A
$${x_{ss}} = \left[ {\matrix{ 0 \cr 0 \cr } } \right]$$
B
$${x_{ss}} = \left[ {\matrix{ { - 3} \cr { - 2} \cr } } \right]$$
C
$${x_{ss}} = \left[ {\matrix{ { - 10} \cr {10} \cr } } \right]$$
D
$${x_{ss}} = \left[ {\matrix{ \infty \cr \infty \cr } } \right]$$
3
GATE EE 1995
+1
-0.3
A system is described by the state equation $$\mathop X\limits^ \bullet = AX + BU$$ , The output is given by $$Y=CX$$ Where $$A = \left( {\matrix{ { - 4} & { - 1} \cr 3 & { - 1} \cr } } \right)\,\,B = \left( {\matrix{ 1 \cr 1 \cr } } \right)\,\,C = \left[ {10} \right]$$

Transfer function $$G(s)$$ of the system is

A
$${s \over {{s^2} + 5s + 7}}$$
B
$${1 \over {{s^2} + 5s + 7}}$$
C
$${s \over {{s^2} + 3s + 2}}$$
D
$${1 \over {{s^2} + 3s + 2}}$$
4
GATE EE 1994
+1
-0.3
The matrix of any state space equations for the transfer function $$C(s)/R(s)$$ of the system, shown below in. Figure is A
$$\left( {\matrix{ { - 1} & 0 \cr 0 & 1 \cr } } \right)$$
B
$$\left( {\matrix{ 1 & 0 \cr 0 & { - 1} \cr } } \right)$$
C
$$\left[ { - 1} \right]$$
D
$$\left[ { 3} \right]$$
GATE EE Subjects
Electric Circuits
Electromagnetic Fields
Signals and Systems
Electrical Machines
Engineering Mathematics
General Aptitude
Power System Analysis
Electrical and Electronics Measurement
Analog Electronics
Control Systems
Power Electronics
Digital Electronics
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