Transformation des systèmes d'Euler-Lagrange : observabilité et systèmes discrets

Abstract : Reasults presented in this thesis concerns the observability and the observer of the nonlinear dynamic systems. It comprises two relatively independent parts. The first part deals with the problem of the transformation of Euler-Lagrange system in order to solve a some interesting problem such as the design of the observer, the output feedback stabilization. Initially, the study is devoted to the development the transformation of Euler-Lugrange systems. We characterize in a rigorous way a class of these systems. We end, in a simpler way, with the results proven by Spong and Bedrossian in 1992. In the second time, we contribute a share to the construction of observers and stabilization by return of exit for a class of systems of Euler-lagrange by transforming such a system into a triangular form. In the second part, we study the problem of the genericity of the strongly differential observabilitv for the controlled discrete svstems with entrv. knowing that the state anddensity (for the Whitney topology) of the whole of the systems strongly dffirential observable when the dimension of the space of the exits is strictly higher than that of the space of the entries, and that one observes (2n + I ) successivev alues of the output, where N is the dimension of the space of the states
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Mohamed Mabrouk. Transformation des systèmes d'Euler-Lagrange : observabilité et systèmes discrets. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2006. Français. ⟨NNT : 2006METZ033S⟩. ⟨tel-01752442⟩

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