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inria-00442081, version 1

Well-posedness, stability and invariance results for a class of multivalued Lur'e dynamical systems

Bernard Brogliato () a, 1, Daniel Goeleven () b, 2

N° RR-7158 (2009)

Résumé : This paper analyzes the existence and uniqueness issues in a class of multivalued Lur'e systems, where the multivalued part is represented as the subdifferential of some convex, proper, lower semicontinuous function. Through suitable transformations the system is recast into the framework of dynamic variational inequalities and the well-posedness (existence and uniqueness of solutions) is proved. Stability and invariance results are also studied, together with the property of continuous dependence on the initial conditions. The problem is motivated by practical applications in electrical circuits containing electronic devices with nonsmooth multivalued voltage/current characteristics, and by state observer design for multivalued systems.

  • a –  INRIA
  • b –  Université de la Réunion
  • 1 :  BIPOP (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
  • INRIA – Laboratoire Jean Kuntzmann
  • 2 :  Institut de REcherche en Mathématiques et Informatique Appliquées (IREMIA)
  • Université de la Réunion
  • Domaine : Mathématiques/Optimisation et contrôle
  • Mots-clés : Lur'e dynamical systems – passivity – invariance – Kato's theorem – maximal monotone operators – variational inequalities – differential inclusions – normal cones
  • Référence interne : RR-7158
 
  • inria-00442081, version 1
  • http://hal.inria.fr/inria-00442081
  • oai:hal.inria.fr:inria-00442081
  • Contributeur : Bernard Brogliato <>
  • Soumis le : Mardi 12 Janvier 2010, 09:26:09
  • Dernière modification le : Mardi 12 Janvier 2010, 09:55:39