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Journal of Control Science and Engineering
Volume 2011, Article ID 967571, 8 pages
http://dx.doi.org/10.1155/2011/967571
Research Article

𝐻 Observers Design for a Class of Continuous Time Nonlinear Singular Systems

CRAN-CNRS, UHP NancyI, IUT de Longwy 186, rue de Lorraine, 54400 Cosnes-et-Romain, France

Received 29 April 2011; Revised 13 July 2011; Accepted 17 July 2011

Academic Editor: Mohamed Zribi

Copyright © 2011 Mohamed Zerrougui 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.

Abstract

This paper considers the problem of 𝐻 observers design for a class of Lipschitz continuous nonlinear singular systems. The method is based on the parameterization of the solution of the generalized Sylvester equations obtained from the estimation errors. Sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given. The approach also unifies the full-order, the reduced-order, and the minimal-order observers design. The solutions are obtained through linear matrix inequalities (LMIs) formulation. A numerical example is given to illustrate our results.