Question: How can I transform a generalized Transfer Function a generalized state space form (preferable with the First Companion Form), and back?

For the sake of presenting an example, let us say that we have the following generalized transfer function: $$ \begin{pmatrix}z\\y\end{pmatrix} = \begin{pmatrix}G(s) &-1\\ H(s)&0\end{pmatrix} \begin{pmatrix}w\\u\end{pmatrix} $$ with $$G(s)=\frac{2}{s+3}$$ and $$H(s)=\frac{s-1}{s+2}$$

I have not been able to find any information on the Internet related to this. I know how to do this when having one transfer function but don't know when having the generalized form.