REAL-POLYNOMIAL BASED IMMITTANCE-TYPE TABULAR STABILITY TEST FOR TWO-DIMENSIONAL DISCRETE SYSTEMS

摘要

The paper proposes a new stability test for two-dimensional (2D) discrete systems. It is a tabular test; that is, it builds for the tested bivariate polynomial of degree (n_1, n_2) a sequence of n_2 (or n_1) bivariate polynomials or matrices (the "2D table") of increasing row and decreasing column sizes. It is an immittance-type test, which means that it uses a three-term recurrence relation to obtain a sequence of matrices with certain symmetry. It differs from some recent immittance tabular tests in that it is derived from the author's stability test for real polynomials instead of complex-coefficient polynomials. In comparison with related 2D stability tests developed before by Karan and Sarisvastava and by Premaratne, it simplifies the number of stability conditions and reduces the overall cost of computation from an exponential to a polynomial order of complexity.