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 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
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
