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Stabilité et commande des systèmes linéaires variant dans le temps aux paramètres incertains

Cristiano Marcos Agulhari 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : The main contributions of this thesis concern the development of methods for the stability analysis and the synthesis of controllers for linear systems, either timevarying or time-invariant. Concerning time-invariant systems, the objective is the synthesis of reduced-order robust controllers for continuous-time systems presenting uncertain parameters. The method presented for the synthesis is based on a twostages technique, in which a stabilizing state-feedback gain is constructed in the first stage and then applied on the second stage to search for the desired controller. Each stage consists in the resolution of conditions based on linear matrix inequalities. In the case of time-varying systems, depending on the amount of available information, two mathematical models may be used. On one hand, if the time-varying elements of the system are not entirely known, one can model the system as function of time-varying parameters, resulting on a polytopic representation. In this case, the stabilization method proposed is based on the two-stages technique, which yields parameter-dependent controllers. The parameters are supposed to be real-time measurable, and the controllers are robust with respect to noises and uncertainties on the measures. On the other hand, if the time-varying dynamics are known, the system may be directly handled without using any parameterization. Two synthesis techniques are proposed in this case: the construction of stabilizing gains by using the state transition matrix, and a synthesis technique derived from a new stability criterion for time-varying systems. The validity of the proposed methods is illustrated through numerical examples, that show the efficiency of the results that can be obtained.
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Cristiano Marcos Agulhari. Stabilité et commande des systèmes linéaires variant dans le temps aux paramètres incertains. Automatique. INSA de Toulouse, 2013. Français. ⟨tel-00822689⟩

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