Realization and Modelling

This paper discusses the problem of parametrization of alI scalar rational fnnctions interpolating a given m y of points, with paramem the complexity, or McMillan degree. The main tool for tackling this problem is the socalled Limmer mmrlr. The L6ma matrix encodes the information about the minimal admissible complexity of the solutions, as a simple function of its rank. The minimal admissible complexity demmihes m him, the remaining, higher, admissible complexities. The computation of the solutions can be carried out both in plynomid and in smte-space frameworks. %is approach to rational inteqa1atioA leads to a gmcdizatiion i f the dassical, system theorctic, &cePtof reali~ati~n of linear dpmical system.