Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 960981, 10 pages
http://dx.doi.org/10.1155/2011/960981
Research Article

Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach

M. Chaabane,1 F. Tadeo,2 D. Mehdi,3 and M. Souissi1

1Research Unit of Industrial Processes Control (UCPI), National Engineering School of Sfax, (ENIS), Route Soukra Km 3.5, BP 1173, 3038 Sfax, Tunisia
2Departamento de Ingenieria de Sistemas y Automatica, Universidad de Valladolid, 47011 Valladolid, Spain
3Laboratory of Automatic and Industrial Informatics (LAII), Higher School of Engineers of Poitiers (ESIP), 40 Avenue du Recteur Pineau, 86022 Poitiers Cedex, France

Received 23 November 2010; Revised 7 February 2011; Accepted 10 March 2011

Academic Editor: J. Rodellar

Copyright © 2011 M. Chaabane 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

The problem of the stabilization of descriptor systems in continuous-time via static output-feedback is studied in this paper and an approach to solve it is proposed. For this, sufficient conditions are derived for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). These conditions are expressed in terms of a strict Linear Matrix Inequality (LMI); so they are tractable using numerical computations. The proposed controller design methodology is based on two steps: the first is dedicated to synthesizing a classical state-feedback controller, which is used as the initial value for the second step, which uses an LMI problem to obtain static output-feedback controllers that give admissibility. Finally, a numerical example is given to illustrate the results.