Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2010, Article ID 724563, 24 pages doi:10.1155/2010/724563 Research Article Improved Results on Robust Stability Analysis and Stabilization for a Class of Uncertain Nonlinear Systems Mohamed Moez Belhaouane, Mohamed Faiez Ghariani, Hela Belkhiria Ayadi, and Naceur Benhadj Braiek Laboratoire d’Etude et Commande Automatique de Processus (LECAP), Ecole Polytechnique de Tunisie, BP 743, 2078 La Marsa, Tunisia Correspondence should be addressed to Mohamed Moez Belhaouane, moez.belhaouane@ept.rnu.tn Received 24 April 2010; Accepted 3 November 2010 Academic Editor: Jerzy Warminski Copyright q 2010 Mohamed Moez Belhaouane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper deals with the problems of robust stability analysis and robust stabilization for uncertain nonlinear polynomial systems. The combination of a polynomial system stability criterion with an improved robustness measure of uncertain linear systems has allowed the formulation of a new criterion for robustness bound estimation of the studied uncertain polynomial systems. Indeed, the formulated approach is extended to involve the global stabilization of nonlinear polynomial systems with maximization of the stability robustness bound. The proposed method is helpful to improve the existing techniques used in the analysis and control for uncertain polynomial systems. Simulation examples illustrate the potentials of the proposed approach. 1. Introduction Being subject of considerable theoretical and practical significance, stability analysis and control of nonlinear dynamic systems have been attracting the interest of investigators for several decades 1–3. The essential aim of robust analysis and nonlinear robust control theory is to internally stabilize the nonlinear plant while maximizing the upper bound on the parametric perturbations, such that the perturbed nonlinear system remains stable, as described in 4–8. However, each of the published approaches on this subject concerns particular classes of nonlinear uncertain systems and there is no standard method to investigate robust stability and stabilization of general high-order nonlinear systems 9– 13. Therefore, in deep contrast with linear analysis and control methods, which are flexible,