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inria-00072309, version 1

## Nonconservative LMI Criteria for Characterization of Delay-Independent Properties of Delay Systems. Application to Stability and Input-Output Analysis of Systems with Complex Parameter

Pierre-Alexandre Bliman 1

N° RR-4278 (2001)

Résumé : This report focuses on delay-independent stability and delay-independent input-output properties (passivity, $H_\infty$ performance, circle criterion, Popov criterion) of delay systems. The main results show that, as it is the case for the usual, rational, systems, the properties under study here may be characterized by solvability of some linear matrix inequalities. The latter are constructed by use of some quadratic Lyapunov-Krasovskii functionals, generalizing a well-known class. The method also applies to the analysis of systems with uncertain complex parameter, for which the results are related to the search for analytic parameter-dependent Lyapunov functions. Illustrative examples are provided.

• 1 :  SOSSO (INRIA Rocquencourt)
• INRIA
• Domaine : Informatique/Autre
• Mots-clés : LINEAR DELAY SYSTEMS / PARAMETER-DEPENDENT SYSTEMS / DELAY-INDEPENDENT STABILITY / QUADRATIC LYAPUNOV-KRASOVSKII FUNCTIONALS / LINEAR MATRIX INEQUALITIES / INPUT-OUTPUT PROPERTIES / PASSIVITY / $H_{\INFTY$ PERFORMANCE / CIRCLE CRITERION / POPOV CRITERION
• Référence interne : RR-4278
• Commentaire : Projet SOSSO

• inria-00072309, version 1
• oai:hal.inria.fr:inria-00072309
• Contributeur :
• Soumis le : Mardi 23 Mai 2006, 20:22:09
• Dernière modification le : Mardi 27 Mars 2007, 11:17:08