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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

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