The second order dynamic system
$\dfrac{dX}{dt}=PX+Qu$
$y=RX$
has the matrices $P$, $Q$ and $R$ as follows:
$P=\begin{bmatrix} -1 & 1\\ 0& -3 \end{bmatrix}$ $Q=\begin{bmatrix} 0\\1 \end{bmatrix}$ $R=\begin{bmatrix} 0 & 1 \end{bmatrix}$
The system has the following controllability and observability properties:
- Controllable and observable
- Not controllable but observable
- Controllable but not observable
- Not controllable and not observable