Stability testing of 2-D digital system polynomials using a modified unit circle test for 1-D complex polynomials

A new algebraic test 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 test for 2-D digital filters and systems. It is based on a modified unit circle zero location test for one variable polynomials with complex coefficients. The test 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 2-D stability implies but that need not be checked to prove 2-D stability are also included.