Dilaver, Kamil Fatih (Univ. of Wuppertal), Tibken, Bernd (Univ. of Wuppertal)

New Numerical Method to the Investigation of Parameter Perturbation Region of Positive Polynomials As a Hypersphere

Scheduled for presentation during the Regular Session "Stability II" (FrP07), Friday, July 28, 2006, 15:45−16:10, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 11, 2025

Abstract

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 in the article is to determine the parameter perturbation region as a hypersphere, for which the considered 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.