[h=3]Canonical realizations[/h] Any given transfer function which is
strictly proper can easily be transferred into state-space by the following approach (this example is for a 4-dimensional, single-input, single-output system)):
Given a transfer function, expand it to reveal all coefficients in both the numerator and denominator. This should result in the following form:
. The coefficients can now be inserted directly into the state-space model by the following approach:
. This state-space realization is called
controllable canonical form because the resulting model is guaranteed to be
controllable (i.e., because the control enters a chain of integrators, it has the ability to move every state).
The transfer function coefficients can also be used to construct another type of canonical form
. This state-space realization is called
observable canonical form because the resulting model is guaranteed to be
observable (i.e., because the output exits from a chain of integrators, every state has an effect on the output
http://en.wikipedia.org/wiki/Realization_(systems)
