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Theses

Méthodologie pour l'analyse et la commande des systèmes à retards

Abstract : This thesis deals with methodologies for the analysis and the control of linear time-delay systems. The first is the geometric approach. The linear time-delay systems can be modelled by a quadruple of matrices with entries over a ring. Then the geometric approach makes it possible to analyze a system with the properties of the modules over a ring. In this part, we develop a well argued analysis of invariance concepts for application in system control. Some logical relationships among various classes of controlled and conditioned invariant modules are established. The second approach is based on algebraic concepts. In this approach, the use of pseudo-polynomials, which are operators with a finite number of derivatives, pointwise and distributed delays, is fundamental. More precisely, the ring of proper and stable fractions of pseudo-polynomials is used in the stabilization problem. The solution gives us a parameterization of all stabilizing controllers and closed-loop transfer matrices. Then, various control problems are addressed, like the disturbance rejection, the disturbance attenuation, the exact or approximated model matching, or the L1 optimal control. Finally, the last approach is about numerical calculus. In this part, the interval analysis is used to solve hard numerical problems, like
the robust stability, the stabilization, or the verification of a gauge for performances and robustness.
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https://tel.archives-ouvertes.fr/tel-00149948
Contributor : Michaël Di Loreto <>
Submitted on : Tuesday, May 29, 2007 - 9:37:34 AM
Last modification on : Wednesday, December 19, 2018 - 3:02:03 PM
Long-term archiving on: : Thursday, April 8, 2010 - 6:08:12 PM

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  • HAL Id : tel-00149948, version 1

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Michaël Di Loreto. Méthodologie pour l'analyse et la commande des systèmes à retards. Automatique / Robotique. Ecole Centrale de Nantes (ECN); Université de Nantes, 2006. Français. ⟨tel-00149948⟩

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