New numerical method for the parameter perturbation region of 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 to solve a large number of problems in robust control, nonlinear contol, convex and non-convex optimization such as determining the robust asymptotic stability of a polynomial system. In this article it is assumed that the polynomials under investigation depend linearly on some parameters. The aim is to determine the whole parameter perturbation region, for which the polynomial is globally positive. The theorem of Ehlich and Zeller is used to achieve this aim. This theorem enables us 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. Two nontrivial examples conclude the paper and show the effectiveness of the presented method