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The second order dynamic system

$\frac{dX}{dt}=PX+Qu$

$y=RX$

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:

  1. Controllable and observable
  2. Not controllable but observable
  3. Controllable but not observable
  4. Not controllable and not observable
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