22055 articles – 15889 Notices  [english version]

hal-00447620, version 1

ON STABILITY OF SETS FOR SAMPLED-DATA NONLINEAR INCLUSIONS VIA THEIR APPROXIMATE DISCRETE-TIME MODELS AND SUMMABILITY CRITERIA

Antonio Loria () 1, Dragan Nesic () 2, Elena Panteley () 1, Andrew Teel 3

SIAM Journal on Control and Optimization 48, 3 (2009) 1888−1913

Résumé : This paper consists of two main parts. In the first part, we provide a framework for stabilization of arbitrary (not necessarily compact) closed sets for sampled-data nonlinear differential inclusions via their approximate discrete-time models. We generalize [19, Theorem 1] in several different directions: we consider stabilization of arbitrary closed sets, plants described as sampleddata differential inclusions and arbitrary dynamic controllers in the form of difference inclusions. Our result does not require the knowledge of a Lyapunov function for the approximate model, which is a standing assumption in [21] and [19, Theorem 2]. We present checkable conditions that one can use to conclude semi-global asymptotic (SPA) stability, or global exponential stability (GES), of the sampled-data system via appropriate properties of its approximate discrete-time model.

  • 1 :  Laboratoire des signaux et systèmes (L2S)
  • UMR8506 CNRS – SUPELEC – Université Paris XI - Paris Sud
  • 2 :  Electrical and Electronic Engineering Department
  • The University of Melbourne
  • 3 :  Center for Control, Dynamical Systems and Computation
  • University of California, Santa Barbara
  • Collaboration : EGIDE, France
  • Domaine : Mathématiques/Systèmes dynamiques
  • Mots-clés : Sampled-data systems – stability – difference inclusions
 
  • hal-00447620, version 1
  • http://hal.archives-ouvertes.fr/hal-00447620
  • oai:hal.archives-ouvertes.fr:hal-00447620
  • Contributeur : Antonio Loria <>
  • Soumis le : Vendredi 15 Janvier 2010, 14:34:28
  • Dernière modification le : Jeudi 19 Avril 2012, 09:30:46