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Définitions et analyse de stabilités pour les systèmes à retard non linéaires

Abstract : The focus of this work is the notion of stability for nonlinear time-delay systems using the Lyapunov time-
domain approach. Five different chapters are devoted to stability properties. After a general introduction,
the second chapter proposes an unconventional approach — based on Lyapunov-Krasovskii functionals —
to the problem of input-output stability. The descriptor form is used to guaranty this stability by solving
linear matricial inequalities (LMI). The next chapter, finite-time stability, is, as far we know, the first work
on this topic for time-delay systems. Specifically several results are given for the stabilization problem on
linear systems with delayed input. The first examples of finite-time stable delayed systems are also given.
The fourth chapter is devoted to the input-to-state stability, which is generalized to the delay case. Sufficient conditions are given to check this stability using Lyapunov-Krasovskii methodology. The interest
of the study based on perturbation problems is highlighted and some interesting perspectives for further research are given. The last part of the work is devoted to the study of practical stability used in solving
the so-called chattering problem in sliding mode control. As the control is rapidly switching, chattering may
appear on the state space — for instance in practical applications when the control dynamics can no longer
be neglected. The chattering problem is carefully analyzed and many simulations are given to demonstrate the advantages of the proposed solution.
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Contributor : Nima Yeganefar <>
Submitted on : Thursday, June 14, 2007 - 1:35:04 PM
Last modification on : Tuesday, November 24, 2020 - 2:18:22 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:27:20 PM


  • HAL Id : tel-00136239, version 2



Nima Yeganefar. Définitions et analyse de stabilités pour les systèmes à retard non linéaires. Automatique / Robotique. Ecole Centrale de Lille; Université des Sciences et Technologie de Lille - Lille I, 2006. Français. ⟨tel-00136239v2⟩



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