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Lois de commande pour une classe de modèles
non linéaires sous la forme Takagi-Sugeno :
Mise sous forme LMI

Abstract : This PhD thesis deals with a particular class of nonlinear models called Takagi-Sugeno.
In spite of their fuzzy background, they can be seen as a collection of linear models
blended by some nonlinear functions.
The stability analysis of this kind of models is investigated through the direct Lyapunov
method and using a quadratic function. This choice is due to its capability to cope with
LMI constraints. These conditions are only sufficient.
Many results are available for these models. The first works were dealing only with
stability and stabilization without any robustness criterion or performances indexes.
Extensions are available on state feedback with observer, descriptor models, uncertain
models, models with delays, dynamic output feedbacks... Some performances criteria are
also considered as the minimization of quadratic criterion, D-Stability, Hinf...
In spite of these results, some problems need to be solved. The quadratic Lyapunov
function approach seems to have reached its limit. Considering that the conditions are
only sufficient, what can be done if they are too restrictive? How to relax a LMI problem
which has no solution? The goal of this thesis is to quit the quadratic framework by
proposing less conservative results than those met in the literature.
Document type :
Complete list of metadatas
Contributor : Alexandre Kruszewski <>
Submitted on : Monday, February 5, 2007 - 1:29:24 PM
Last modification on : Wednesday, December 2, 2020 - 1:26:01 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:11:07 PM


  • HAL Id : tel-00128986, version 1


Alexandre Kruszewski. Lois de commande pour une classe de modèles
non linéaires sous la forme Takagi-Sugeno :
Mise sous forme LMI. Automatique / Robotique. Université de Valenciennes et du Hainaut-Cambresis, 2006. Français. ⟨tel-00128986⟩



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