Stability of Interval Two–Variable Polynomials and Quasipolynomials via Positivity

Abstract

Stability of two-dimensional polynomials arises in fields as diverse as 2D digital signal and image processing ([11], [7], [18]), time-delay systems [14], repettitive, or multipass, processes [24], and target tracking in radar systems. For this reason, there have been a large number of stability criteria for 2D polynomials, which have been surveyed and discussed in a number of papers ([13], [22], [9], [4], [5], [21]). In achieving the maximal efficiency of 2D stability tests, the reduction of algebraic complexity offered by the stability criteria in [26] has been useful. Apart from some minor conditions, the criteria convert stability testing of a 2D polynomial to testing of only two 1D polynomials, one for stability and the other for positivity.