When converting a transfer function model to a state-space model, the number of states is equal to the cumulative order of the entries in the state-space model.
$$H(s)=\begin{bmatrix}
\frac{s+1}{s^3+3s^2+3s+2} \\
\frac{s^2 + 3}{s^2 + s + 1}
\end{bmatrix}$$
For example, this S-domain transfer function has one input S. It has 2 outputs, because there are 2 rows in the matrix. It also has 5 internal states, because the order of the top equation is 3 and the order of the bottom equation is 2.
[[MIMO Transfer Functions]] – H(s) is an example of a MIMO TF
[[Converting a Transfer Function to an Observable Canonical State-Space Model]]
[[Converting a Transfer Function to a Controllable Canonical State-Space Model]]
- StatespaceModelMATLAB