Model Reduction of Multidimensional Linear Shift- Invariant Recursive Systems Using Pad Techniques*

Abstract. This paper describes a very flexible "general order" multivariate Padd approximation technique for the model reduction of a multidimensional linear shift-invariant recursive system, i.e., a system characterized by a multivariate rational transfer function. The technique presented allows full control of the regions of support in numerator and denominator of the reduced system and also admits a nonbranched continued fraction representation for an easy realization of the model. The method presented here overcomes some of the problems of related approaches to mode/reduction of multidimensional linear recursive systems. Different rational approximants can be introduced to compute the reduced model, but a drawback is that these approximants are not always readily available in continued fraction form for immediate implementation of the reduced system. Also multibranched continued fractions can be used to approximate the transfer function, but it was pointed out that the regions of support of numerator and denominator blow up rapidly as one considers successive convergents. Both these problems are overcome here.