For each of the transfer functions below, write the state equations in both control and observer canonical form. In each case, draw a block diagram and give the appropriate expressions for \(\mathbf{A}, \mathbf{B}\), and \(\mathbf{C}\)

\[
\begin{aligned}
& \text { (a) } \frac{s^{2}+1}{s^{2}\left(s^{2}-1ight)} \text { (control of an inverted pendulum) } \\
& \text { (b) } \frac{3 s+4}{s^{2}+2 s+2}
\end{aligned}
\]