Belhaouane, Mohamed Moez; Ghariani, Mohamed Faiez; Ayadi, Hela Belkhiria; Benhadj Braiek, Naceur Improved results on robust stability analysis and stabilization for a class of uncertain nonlinear systems. (English) Zbl 1206.93082 Math. Probl. Eng. 2010, Article ID 724563, 24 p. (2010). Summary: 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 potential of the proposed approach. Cited in 1 Document MSC: 93D09 Robust stability 93D21 Adaptive or robust stabilization 93C10 Nonlinear systems in control theory Keywords:robust stability analysis; robust stabilization; polynomial system; robustness measure; stability robustness bound Software:Optimization Toolbox PDFBibTeX XMLCite \textit{M. M. Belhaouane} et al., Math. Probl. Eng. 2010, Article ID 724563, 24 p. (2010; Zbl 1206.93082) Full Text: DOI EuDML References: [1] S. Jannesari, “Stability analysis and stabilization of a class of nonlinear systems based on stability radii,” in International Conference on Control, Control, vol. 1, pp. 641-645, Swansea, UK, 1998. [2] J. Zhijian and W. Long, “Robust stability and stabilization of a class of nonlinearswitched systems,” in Proceedings of the 25th IASTED International Conference on Modelling, Indentification, and Control, pp. 37-42, Lanzarote, Spain, 2006. [3] M. S. Mahmoud and N. B. 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