Stabilisation de trajectoires, ajout d'intégration, commandes saturées

Abstract : The general topic of the first part of our work is the global asymptotic stabilization of non linearsystems.Westudysystemswhichgeneralizetheform x ̇=h(y,u),y ̇=f(y,u),i.e.where the state components x integrate functions of the others components y and the inputs u. We give sufficient conditions under which global asymptotic stabilizability of the y-subsystem (resp. by saturated control) implies global asymptotic stabilizability of the overall system (resp. by saturated control). This is established by an explicit Lyapunov design of the control law. This result is established with the functions f and h depending in some way also on x. We show how it serves as a basic tool to be used, may be recurrently, to deal with more complex systems. In particular the stabilization problem of the so called feedforward systems is solved this way. We illustrate how this method works by applying it to various practical systems. In the second part of our work, we adapt the techniques displaid in the firts part to the problem of global asymptotic stabilization of a reference trajectory for feedforward systems of a slightly less general form. A particular attention is devoted to the issue of uniform stability. This time again, a pratical example allows us to illustrate our results.
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  • HAL Id : pastel-00838918, version 1

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Frédéric Mazenc. Stabilisation de trajectoires, ajout d'intégration, commandes saturées. Automatique / Robotique. École Nationale Supérieure des Mines de Paris, 1996. Français. ⟨NNT : 1996ENMP0622⟩. ⟨pastel-00838918⟩

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