A system is described as follows: where [ begin{aligned} dot{x} & =mathrm{A} x+mathrm{B} u y &

Question:

A system is described as follows:

where

\[
\begin{aligned}
\dot{x} & =\mathrm{A} x+\mathrm{B} u \\
y & =\mathrm{C} x \\
\mathrm{~A} & =\left[\begin{array}{ll}
1 & 1 \\
0 & 1
\end{array}ight], \quad \mathrm{B}=\left[\begin{array}{l}
\alpha_{1} \\
\alpha_{2}
\end{array}ight], \quad \mathrm{C}=\left[\begin{array}{ll}
\beta_{1} & \beta_{2}
\end{array}ight]
\end{aligned}
\]

What restrictions should be imposed on $\alpha_{1}, \alpha_{2}, \beta_{1}$ and $\beta_{2}$ so that the system is completely controllable and observable.