A new proof of the Jury test

The problem of determining the root distribution of a real polynomial with respect to the unit circle, in terms of the coefficients of the polynomial, was solved by Jury in 1964. The calculations were presented in tabular for m (Jury's table) and were later simplified by Raible in 1974. This result i s now classical and is as important in the stability analysis of digital co ntrol systems as its continuous time counterpart, the Routh Hurwitz criteri on is for the stability analysis of continuous time control systems. Most t exts on digital control state the Jury test but avoid giving the proof. In this paper we give a simple, insightful and new proof of the Jury test. The proof is based on the behavior of the root-loci of an associated family of polynomials that was introduced in recent literature. The proof reveals cl early the mechanism underlying the counting of the roots within and without the unit circle. (C) 1999 Elsevier Science Ltd. All rights reserved.