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Schémas d'intégration dédiés à l'étude, l'analyse et la synthèse dans le formalisme Hamiltonien à ports

Abstract : This thesis work dealing with finite dimensional approximation of infinite dimension system. The class considered is that of Hamiltonian systems in ports. We study initially ordinary differential equations systems. Based on an energy integrator, we define a class of discrete passive dynamics is invariant interconnection. We obtain the stability conditions (LMI) for dynamic network in the presence of delays and uncertainties, and propose a method of stabilizing energy synthesis. These developments were experimentally validated by the implementation of an energy control a power converter (Buck). We then study the Hamiltonian formalism in infinite dimensions. We offer an approximation that combines a semi-discretization and an energy integrator. The mixed composability is studied and a method of synthesis IDA-PBC was developed. All the obtained results are numerically illustrated in the manuscript.
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Saïd Aoues. Schémas d'intégration dédiés à l'étude, l'analyse et la synthèse dans le formalisme Hamiltonien à ports. Mathématiques générales [math.GM]. INSA de Lyon, 2014. Français. ⟨NNT : 2014ISAL0121⟩. ⟨tel-01175869⟩

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