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
$$\left[ { 3} \right]$$
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