Identification of an impulse response through a model of ARX structure

Polynomial parametric models of ARX structure are becoming increasingly popular for characterizing heat transfer for linear thermal systems with time invariant coefficients. This stems from their robustness when applied to inverse problems, either for model reduction, for experimental model identification or for inverse input problems. Their parsimonious character allows to get residuals of very low levels with a limited number of coefficients. This paper shows, on a theoretical algebraic basis, that ARX models can be deduced from convolutive models.