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Contribution à la stabilité et la stabilisation des systèmes non linéaire

Abstract : This theisis is a contribution to the problems of the stability (in sens of Lagrange) and the stabilization by feedback law of nonlinear systems. It concerns mainly the homogeneous systems. A first result concerns the stability in sens of Lagrange of a class of tridimensional quadratic systems. More precisely, we study the class of vector fields on the cylinders. In the second part of this work, we present a necessary and suffisante condition for the stabilization by means of a continuous feedback of polynomial homogeneous system with respect to a dilation. In the case of a standard dilation, we propose explicitely polynomial stabilizing feedback. Finally, the least kind of results concerns the proplem of the stabilization by a dynamic feedback. We give a new proof of a well-known in the theory of stabilization called "integrators lemma". This new approch permits to give explicitely the stabilizing feedback for the augumented system, in some situations when the classical method shows only the existence. Moreover, the proposed feedback law is more smooth
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Hamid Jghima. Contribution à la stabilité et la stabilisation des systèmes non linéaire. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1996. Français. ⟨NNT : 1996METZ017S⟩. ⟨tel-01777129⟩

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