A generalisation of Jury’s conjecture to arbitrary dimensions and its proof

Abstract

In 1986 E. I. Jury conjectured by analogy to the theory of digital filters that a two-dimensional analog filter is BIBO stable if its transfer function is of the form H = 1/P, where P is a very strict Hurwitz polynomial (VSHP). In this article we prove a generalisation of Jury’s conjecture to r-dimensional analog filters (r ≥ 2) with proper transfer function H = Q/P, where the denominator P is a robustly stable polynomial, i.e., a strict Hurwitz polynomial which retains this property under small variations of its coefficients. In the bivariate case these polynomials are the VSHPs.