Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 608374, 21 pages
doi:10.1155/2010/608374
Research Article

New Dilated LMI Characterization for the Multiobjective Full-Order Dynamic Output Feedback Synthesis Problem

Jalel Zrida1,2 and Kamel Dabboussi1,2

1Département de Génie Electrique, Ecole Supérieure des Sciences et Techniques de Tunis, 5 Avenue Taha Hussein, BP 56, Tunis 1008, Tunisia
2Unité de Recherche SICISI, Ecole Supérieure des Sciences et Techniques de Tunis, 5 Avenue Taha Hussein, BP 56, Tunis 1008, Tunisia

Received 23 April 2010; Revised 17 August 2010; Accepted 17 September 2010

Academic Editor: Kok Teo

Copyright © 2010 Jalel Zrida and Kamel Dabboussi. 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 introduces new dilated LMI conditions for continuous-time linear systems which not only characterize stability and 𝐻 2 performance specifications, but also, 𝐻 ∞ performance specifications. These new conditions offer, in addition to new analysis tools, synthesis procedures that have the advantages of keeping the controller parameters independent of the Lyapunov matrix and offering supplementary degrees of freedom. The impact of such advantages is great on the multiobjective full-order dynamic output feedback control problem as the obtained dilated LMI conditions always encompass the standard ones. It follows that much less conservatism is possible in comparison to the currently used standard LMI based synthesis procedures. A numerical simulation, based on an empirically abridged search procedure, is presented and shows the advantage of the proposed synthesis methods.