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Mathematical Problems in Engineering
Volume 2009, Article ID 486470, 22 pages
Research Article

Robust Stabilization Approach and 𝐻 Performance via Static Output Feedback for a Class of Nonlinear Systems

Laboratoire d'Analyse et de Commande des Systèmes (LACS), Ecole Nationale des Ingénieurs de Tunis (ENIT), P. B. 37, Le Belvédère, CP 1002 Tunis, Tunisia

Received 17 November 2008; Revised 18 February 2009; Accepted 12 March 2009

Academic Editor: Shijun Liao

Copyright © 2009 Neila Bedioui 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 stability and stabilization problems for a class of discrete-time nonlinear systems. The systems are composed of a linear constant part perturbated by an additive nonlinear function which satisfies a quadratic constraint. A new approach to design a static output feedback controller is proposed. A sufficient condition, formulated as an LMI optimization convex problem, is developed. In fact, the approach is based on a family of LMI parameterized by a scalar, offering an additional degree of freedom. The problem of performance taking into account an 𝐻 criterion is also investigated. Numerical examples are provided to illustrate the effectiveness of the proposed conditions.