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| HAL : hal-00697498, version 1 |
| Fiche détaillée |  Récupérer au format |
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| 10th IFAC Workshop on Time Delay Systems, Boston : États-Unis (2012) |
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| On the use of the Wirtinger inequalities for time-delay systems |
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| Alexandre Seuret 1, 2Frédéric Gouaisbaut 3 |
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| (22/06/2012) |
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| The paper addresses the stability problem of linear time delay system. In the literature, the most popular approach to tackle this problem relies on the use of Lyapunov-Krasovskii functionals. Many results have proposed new functionals and techniques for deriving less and less conservative stability conditions. Nevertheless, all these approaches use the same trick, the well-known Jensen's inequality which generally induces some conservatism difficult to overcome. In light of those observations, we propose to reduce the conservatism of Lyapunov-Krasovskii functionals by introducing new classes of integral inequalities called Wirtinger inequalities. This integral type inequality is rstly shown to encompass Jensen's inequality and is then employed to derive new stability conditions. To this end, a slightly modi ed Lyapunov functional is proposed. Several examples illustrate the e ectiveness of our methodology. |
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| 1 : | Grenoble Images Parole Signal Automatique (GIPSA-lab) |
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CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| 2 : | NeCS (INRIA Grenoble Rhône-Alpes / Gipsa-lab) |
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CNRS : UMR5216 – INRIA – Gipsa-lab – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG) |
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| 3 : | Laboratoire d'analyse et d'architecture des systèmes (LAAS) |
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CNRS : UPR8001 – Université Paul Sabatier [UPS] - Toulouse III – Institut National Polytechnique de Toulouse - INPT – Institut National des Sciences Appliquées (INSA) - Toulouse |
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| LAAS-MAC |
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| Domaine | : | Sciences de l'ingénieur/Automatique / Robotique |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00697498, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00697498 | |
| oai:hal.archives-ouvertes.fr:hal-00697498 | |
| Contributeur : Alexandre Seuret | |
| Soumis le : Mardi 15 Mai 2012, 15:18:24 | |
| Dernière modification le : Vendredi 12 Avril 2013, 15:38:40 | |
