Skip to Main content Skip to Navigation

Diverses méthodes pour des problèmes de stabilisation

Abstract : In this thesis, we study some problems of stabilization in control theory for three different class of systems. First, for the non-linear finite-dimensional systems in presence of noise, we introduce a class of hybrid controllers with a mixed continuous/discrete state. Given a system with a globally asymptotically controllable equilibrium, we prove that there exists such a control such that the equilibrum is globally asymptotically stable with a robustness property with respect to small perturbations. For the chained systems we explicit such a feedback with only one discrete variable. We give also a hybrid control and a time-varying control which unit robustly any pair of continuous feedbacks and renders the origin a globally asymptotically stable equilibrium. Secondly, we study the stabilization problem of the tank containing a fluid subject. It is subject to a horizontal move. It is a infinite-dimensional control problem because we describe the system by using the shallow water equations which are hyperbolic partial differential equations. We use a Lyapunov approach to propose some feedbacks which numerically stabilize locally and asymptotically the origin of the closed-loop system. Finally, we study the problems of stabilization of the origin of a linear, finite-dimensional system with a uncertainty of the data of the system. We apply the methods of the numerical resolution of robust linear matrix inequalities to a industrial problem.
Document type :
Complete list of metadatas
Contributor : Christophe Prieur <>
Submitted on : Thursday, November 7, 2002 - 2:30:44 PM
Last modification on : Thursday, April 11, 2019 - 1:11:17 AM
Long-term archiving on: : Friday, April 2, 2010 - 6:19:04 PM


  • HAL Id : tel-00001928, version 1



Christophe Prieur. Diverses méthodes pour des problèmes de stabilisation. Mathématiques [math]. Université Paris Sud - Paris XI, 2001. Français. ⟨tel-00001928⟩



Record views


Files downloads