New Dilated LMI Characterization for the Multiobjective Full-Order Dynamic Output Feedback Synthesis Problem
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Research Article New Dilated LMI Characterization for the Multiobjective Full-Order Dynamic Output Feedback Synthesis Problem Jalel Zrida1, 2 and Kamel Dabboussi1, 2 1
Ecole Sup´erieure des Sciences et Techniques de Tunis, 5 Taha Hussein Boulevard, BP 56, Tunis 1008, Tunisia 2 Unit´e de Recherche SICISI, Ecole Sup´erieure des Sciences et Techniques de Tunis, 5 Taha Hussein Boulevard, BP 56, Tunis 1008, Tunisia Correspondence should be addressed to Kamel Dabboussi, dabboussi [email protected] Received 23 April 2010; Revised 17 August 2010; Accepted 17 September 2010 Academic Editor: Kok Teo Copyright q 2010 J. Zrida and K. 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. This paper introduces new dilated LMI conditions for continuous-time linear systems which not only characterize stability and H2 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.
1. Introduction The impact of linear matrix inequalities on the systems community has been so great that it dramatically changed forever the usually utilized tools for analyzing and synthesizing control systems. The standard LMI conditions benefited greatly from breakthrough advances in convex optimization theory and offered new solutions to many analysis and synthesis problems 1–3. When necessary and sufficient LMI conditions are not possible, as it is the case for the static output control 4, 5, the multi-objective control 6–8, or the robust control 9–12 problems, sufficient conditions were provided, but were known to be overly conservative. Some dilated versions of LMI conditions have first appeared in the literature
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Journal of Inequalities and Applications
in 13, wherein some robust dilated LMI conditions were proposed for some class of matrices. Since then, a flurry of results has been proposed in both the continuous-time 6, 7, 10, 14–17 and the discrete-time systems 5, 14, 18–20. These conditions offer, though, no particular advantages for monoobjective and precisely known systems, but were found to greatly reduce conservatism in the multi-objective 6–8, 19 and the robust control problems 9, 10, 14–16, 18, 19. In this respect, an interesting extension for the utilization of these dilated
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