Let's say we have a system $S$ which we model by a nth order ODE and its Lapace transform a transfer function $H(s)$.
A state space model $(A,B,C,D)$ is another way of modeling this and we have the canonical forms among many other ways to model it.
The question is weather there are restrictions in choosing state variables? According to the definitons of them it donst look like it has have to be related to the in/out-put equations very strongly.
Are we simply satisfied if the transfer functions agree and that the output $y$ is a sum of the states?
In the somewhat similar situation for ODE's when you go from ODE to first order system the systems are equivalent but it donst seem that the restiction is the same here in chooing state variables.