Journal of Applied Mathematics
Volume 2012 (2012), Article ID 812920, 13 pages
Research Article

Sufficient Dilated LMI Conditions for 𝐻 Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems

Ecole Supérieure des Sciences et Techniques de Tunis, 5 Rue Taha Hussein, BP 56 Bab Menara, 1008 Tunis, Tunisia

Received 16 September 2011; Revised 23 November 2011; Accepted 24 November 2011

Academic Editor: C. Conca

Copyright © 2012 Kamel Dabboussi and Jalel Zrida. 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.


New sufficient dilated linear matrix inequality (LMI) conditions for the 𝐻 static output feedback control problem of linear continuous-time systems with no uncertainty are proposed. The used technique easily and successfully extends to systems with polytopic uncertainties, by means of parameter-dependent Lyapunov functions (PDLFs). In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with even more relaxed structure are employed. It is shown that these slack variables provide additional flexibility to the solution. It is also shown, in this paper, that the proposed dilated LMI-based conditions always encompass the standard LMI-based ones. Numerical examples are given to illustrate the merits of the proposed method.