An elementary proof of the Jury test for real polynomials

As is well known the Jury test has been considered as the most typical way of determining the Schur stability of real polynomials and is introduced in most textbooks on digital control engineering. Its original proof is based on Rouché's theorem. Recently Keel et al. gave a simple proof of the Jury test using Raible's simplified table. In this paper we provide another elementary proof of the Jury test. Contrary to that of Keel et al., the proof is carried out directly for the original form of the Jury test.