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Sur la robustesse des systèmes linéaires incertains : approche quadratique, retour de sortie

Abstract : In this thesis, robust control of linear systems with parametric uncertainty is considered. The approach developed relies on the quadratic stability concept which is based on the quest for and exploitation of Lyapunov functions quadratic with respect to the state. This thesis, particularly, focuses on the design of dynamic output feedback controllers, that is, controllers based on the treatment of the information available in the measured output of the system. Also, focus is placed on the parametric polyhedric type of uncertainty in the model (interval matrices). A brief review of some of the results on state feedback robust control by the quadratic approach provides the essential elements to formally introduce the dynamic output feedback control problem for uncertain systems : structured and unstructured uncertainty. Some known results for ¿norm bounded¿ unstructured uncertain systems are recalled and original results in the form of necessary conditions and sufficient conditions are presented. It is shown that polyhedric uncertain is the extreme case of norm bounded structured uncertainty. In the face of polyhedric uncertainty, an iterative algorithm to determine a Luenberger type dynamic output feedback is proposed. The algorithm takes advantage of the biconvex nature of the sufficient condition of quadratic stability with respect to the control law and to the Lyapunov function. This result allows, similarly, the computation of a (maximum) uncertain domain (some sort of gain margin of the compensator). These results, originally developed for continuous systems, are later extended to uncertain discrete linear systems and to the pole placement in circular regions of the ¿s-plane¿, this latter whit high practical interest since it allows manipulation of the dynamics of the controlled system. Other (robust) performance measures are taken into consideration : H2 (quadratic criteria) and H¿ (worst case) with the same quadratic approach.
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Contributor : Emilie Marchand <>
Submitted on : Tuesday, April 3, 2007 - 2:21:04 PM
Last modification on : Thursday, June 10, 2021 - 3:05:23 AM
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  • HAL Id : tel-00139742, version 1


William Colmenares. Sur la robustesse des systèmes linéaires incertains : approche quadratique, retour de sortie. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 1996. Français. ⟨tel-00139742⟩



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