Robust Stability of Discrete Polynomials with Polynomic Structure of Coefficients

Abstract

A method for Schur robust stability analysis of polynomials with polynomic structure of their coefficients is presented in this paper. The presented method tests the stability in the coefficient space and is based on the Modified Jury criterion. Coefficients of this table are multivariate polynomial functions, whose positivity is tested by Sign-decomposition. This is a method which makes it possible to test positivity of some set of multivariate functions on a convex set. Another approach consists in using linear fractional transformation of discrete polynomials into continuous polynomials and then in using the Modified Routh criterion or the Hurwitz criterion together with Sign-decomposition for robust stability analysis. To determine elements of any table a new procedure based on fast Fourier transform for multivariate polynomial multiplication is used. Both methods are resulting in a necessary and sufficient condition. They are demonstrated on an easy example and compared from computational point of view.