Quelques resultats de stabilisation robuste. applications à la commande

Abstract : We study the problem of robustness of the boundedness and the stability properties for nonlinear systems. The first part is devoted to the formulation of sufficient conditions guaranteeing that the properties of boundedness or stability of the actual system can be obtained from those of the model. The first condition we propose is based on the technique of gain functions. It is related to the notion SpES which is a natural generalization of the input-to-state stability (ISS) introduced by E.D. Sontag. For a system composed of interconnected subsystems, the notion SpES allows us to state a generalized small-gain theorem which contains a result on input-ouput stability and another one on stability in the Lyapunov sense of the internal variables. This theorem generalizes the small monotone gain theorem recently found by Mareels-Hill. The second condition is built on Lyapunov techniques. This condition called GUEC quantifies a kind of distance and permits us to take into account potentially a large class of perturbations. This part is closed by a comparison of these two new characterizations with three more classic characterizations : total stability, singular perturbations and regular perturbations. The second part is concerned with the control design to satisfy the conditions stated in the first part. We start by showing that, for a class of nonlinear systems, we can elaborate control laws to fulfill the conditions of the generalized small-gain theorem. In particular, some problems of global stabilization by output feedback and by partial-state feedback are solved. Then we give an application of the small-gain theorem to a class of systems subject to parametric and dynamic uncertainties. We design adaptive controllers which guarantee the boundedness of the solutions. Finally, for the purpose of getting asymptotic convergence of the solutions, we introduce a dynamic normalizing signal which informs about the size of the unmodelled effects.
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Zhong-Ping Jiang. Quelques resultats de stabilisation robuste. applications à la commande. Automatique / Robotique. École Nationale Supérieure des Mines de Paris, 1993. Français. ⟨NNT : 1993ENMP0404⟩. ⟨pastel-00838279⟩

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