State space models are not unique in that one can get models with equivalent input/output behaviour but very different state definitions. This resources introduces the concept of equivalence and shows how one can from state space models with a desirable structure. Readers are reminded that changing the model structure and changing the states may mean there is no longer a physical interpretation for the model states. Also looks at transformation possible using an eigenvalue/vector decomposition which exposes the underlying behaviours as being linked to the eigenvalues.