control systems - state space representation using transfer functions
There are several ways to convert a transfer function into a state space representation. They lead to apparently different results, but retain the same essential information.

Possible representations:

_  First companion form (controllable canonical form).

_  Jordan canonical form.

_  Alternate first companion form (Toeplitz first companion form).

_  Second companion form (observable canonical form).

There is no single set of state variables which describe a given system. Different sets of variables can be chosen. It is possible to transform one set into another (ie linear combination).