New numerical algorithms for the investigation of robust positivity of polynomials with uncertain parameters

Abstract

This paper addresses the problem of global robust positivity for polynomials with coefficients depending linearly on uncertain parameters. Based on considerations from real algebraic geometry, numerical LMI solvers and the theorem of Ehlich and Zeller we propose two algorithms for the estimation of the convex region in the space of coefficients, for which a polynomial is globally positive. Illustrative examples are given.