New numerical method for the polynomial positivity invariance under coefficient perturbation

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. We assume that the polynomials under investigation depend linearly on some parameters. Our aim is to determine the parameter perturbation region as a hypercube, for which the polynomial is globally positive. We use the theorem of Ehlich and Zeller 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 we calculate inner and outer approximations to the relevant perturbation region which is a hypercube. One nontrivial example concludes the paper and shows the effectiveness of the presented method.