Approximation of polynomial state-affine discrete-time systems

In this paper, a method is developed for finding the coefficients of a lower order polynomial state-affine discrete-time model with a specified structure which gives the best approximation, in least squares sense, to the zero-state input-output map of a given polynomial state-affine discrete-time system over a finite interval. This is done through an extension of the time-domain design theory for linear recursive digital filters. The proposed method does not require complex computations since the coefficients in the model are found by iteratively solving linear equations. Two examples are given to illustrate the utility of the model and proposed method.