The computer implementation of bilinear s-z transformation using new continued fraction algorithms

Abstract

The application of continued fractions to the bilinear transformation of polynomials is introduced. The operations to perform the transformation are continued fraction expansion in the s domain and continued fraction inversion in the z domain. Novel algorithms and computer programs to implement the expansion and the inversion are presented. In particular, the expansion algorithm provides closed forms for the continued fraction quotients in terms of the corresponding rational function coefficients. It is shown that the computer implementation of this algorithm iteratively results in a simple procedure for evaluating the quotients by hand and saves considerable computation time. It is especially noted that the algorithmic character of continued fractions leads to a simple systematic computation scheme. The proposed method of bilinear transformation capitalizes on the knowledge gained in continuous-time stability theory and introduces the topic of z-domain continued fractions and their applications. Numerical examples and computer data are provided. >