Consider the following dynamic system $S$ :

$x^{}(t)=\left[\begin{array}{ccc}0& -1& 0\\ -1& 0& 0\\ 1& 1& 1\end{array}\right]x(t)+\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right]u(t)$;$,y(t)=\left[\begin{array}{ccc}1& 0& 1\end{array}\right]x(t)$

Is $S$ controllable $($justify your answer$)?$ if so$,$ find the controllability similarity transform matrix.

Is $S$ observable $($justify your answer$)?$ if so$,$ find the observability similarity transform matrix.

Find the eigenvalues and eigenvectors of the state matrix of $S.$ Is a canonical diagonal form possible to obtain? if so$,$ provide the corresponding similarity transform matrix.