Abstract

A new algebraic for determining whether all zeros of a two-variable (two-dimensional, 2-D) polynomial reside in the interior of a unit bi-circle is developed. The method provides a stability for digital filters and systems. It is based on a modified unit circle zero location for one variable polynomials with complex coefficients. The comprises a 2-D table in the form of a sequence of centro-symmetric matrices and an accompanying set of necessary and sufficient conditions posed on it. The sequence is constructed by a three-term recursion of matrices or two variable polynomials. The set of necessary and sufficient conditions, at its minimal setting, consists of only one positivity test plus a standard 1-D stability test. Additional useful stability conditions that stability implies but that need not be checked to prove stability are also included.

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