The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{
{ - 1} & 1 \cr
0 & { - 3} \cr
} } \right]\,\,Q = \left[ {\matrix{
0 \cr
1 \cr
} } \right]$$
$$R = \left[ {\matrix{
0 & 1 \cr
} } \right]$$ The system has the following controllability and observability properties:
A
Controllable and observable
B
Not controllable but observable
C
Controllable but not observable
D
Not controllable and not observable