Discussion about sliding mode algorithms, Zeno phenomena and observability

Lei Yu 1 Jean-Pierre Barbot 2, 3 Djamila Benmerzouk 4 Driss Boutat 5 Thierry Floquet 3, 6 Gang Zheng 3
1 ECS-Lab
ECS-Lab - Électronique et Commande des Systèmes Laboratoire
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 Departement de Mathématique
Département de Mathematiques [Tlemcen]
6 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : This chapter is devoted to a discussion about the relations between first and high order slidingmode algorithms and both types of Zeno (Chattering and Genuinely) behaviors of switched dynamical systems. Firstly, the Henstock-Kurzweil integral is recalled in order to set up the problem of switched systems with Zeno phenomena, which enables to include Filippov solution and take into account some singularities. Then, observer designs based on the well-known super twisting algorithm are proposed. For this kind of problems, the importance of finite time convergence of the observation error is studied, and some simulations are given to highlight the discussion. Lastly, the two tanks example is given in order to point out the differences between both Zeno phenomena types, to show that there is life after Zeno and that a higher order sliding mode observer can be efficient before, during and after both Zeno phenomena types.
Type de document :
Chapitre d'ouvrage
Fridman, Leonid; Moreno, Jaime; Iriarte, Rafael (Eds.). Lecture Notes in Control and Information Sciences, 2012, Volume 412, Springer, 2012
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Lei Yu, Jean-Pierre Barbot, Djamila Benmerzouk, Driss Boutat, Thierry Floquet, et al.. Discussion about sliding mode algorithms, Zeno phenomena and observability. Fridman, Leonid; Moreno, Jaime; Iriarte, Rafael (Eds.). Lecture Notes in Control and Information Sciences, 2012, Volume 412, Springer, 2012. 〈hal-00750621〉

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