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Quelques résultats sur la stabilisation des systèmes non linéaires par estimation et retour d'état

Abstract : The aim of this thesis is the study of some problems on the stabilization of nonlinear systems using an observer configuration. In the first part we give necessary and sufficient conditions, algebraically computable, for the global asymptotic stabilization of homogeneous affine systems. It turns out that the stabilizability is equivalent to the asymptotic controllability to the origin. In the tthird chapter we deal with planar bilinear systems and we consider constained stabilizing homogenous feedback law of degree zero. In the case when B has no zero a simple eigenvalus we prove that the system is stabilizable using a like Kalman observer configuration. In the last chapter we deal with single-input-single-output systems. We propose a low-gain Pi-controller which stabilzes and regulates the system. Our result generalizes the previous one of Pohjolainen (1982) in that the semigroup is not necessarily holomorphic. A numerical example will be given to illustrate the application of the theory
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Hamadi Jerbi. Quelques résultats sur la stabilisation des systèmes non linéaires par estimation et retour d'état. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1994. Français. ⟨NNT : 1994METZ014S⟩. ⟨tel-01776050⟩

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