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
$${1 \over {{s^2} + 3s + 2}}$$
2
GATE EE 1994
MCQ (Single Correct Answer)
The matrix of any state space equations for the transfer function $$C(s)/R(s)$$ of the system, shown below in. Figure is
Consider a second order system whose state space representation is of the form $$\mathop X\limits^ \bullet = AX + BU.$$ If $$\,{x_1}\,\,\left( t \right)\, = {x_2}\,\left( t \right),$$ then system is
A
controllable
B
uncontrollable
C
observable
D
unstable
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