Investigation of Parameter Perturbation Region for Positive Polynomials

In this paper the robust positivity of polynomials under coefficient perturbation is investigated. This robust positivity of polynomials can be used for polynomial systems in order to determine the robust asymptotic stability of the system. It is assumed that the polynomials under investigation depend linearly on some parameters. The aim in the article is to determine the parameter perturbation region as a hypersphere, for which the polynomial is globally positive. The theorem of Ehlich and Zeller is used to achieve this aim. This theorem enables to give conditions in the parameter space for global positivity. These conditions are linear inequalities. By means of these inequalities an inner and an outer approximation are calculated to the relevant perturbation region which is a hypersphere. Two nontrivial examples conclude the paper.