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Mathematical Problems in Engineering
Volume 2006, Article ID 39367, 15 pages

Stability and stabilization of continuous descriptor systems: An LMI approach

1Automatic Control Unit, Sfax Preparatory Institute for Engineering Studies (IPEIS), Sfax University, BP 805, Sfax 3018, Tunisia
2Laboratory of Automatic Control and Computer Science for Industry (LAII), Higher Engineering School of Poitiers (ESIP), University of Poitiers, 40 Avenue du Recteur Pineau, Poitiers Cedex 86022, France

Received 8 February 2005; Revised 19 November 2005; Accepted 24 January 2006

Copyright © 2006 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.


This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free). Based on this, the state-feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.