Comparison between some stability criteria of discrete-time filters

Routh´s algorithm is written in the form of polynomial recursion and transposed for testing stability in the wide sense of discrete-time linear systems. The algorithm obtained is a three-term recursion of symmetric polynomials. This recursion easily gives both the coefficients appearing in the continued fraction expansion associated to a given polynomial in the z-domain, and a computation scheme for the bilinear transformation of polynomials. Finally, this recursion is compared to other algorithms already known for testing stability