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Discrétisation des systèmes de Lur'e: stabilisation et consistance

Abstract : Recent studies dealing with discrete-time (switched) Lur’e systems involve an adapted Lur’e type function exhibiting possibly non-convex and disconnected level sets. These properties raise fundamental issues in the case of discrete-time Lur’e system obtained by the sampling of a continuous time one. This PhD thesis aims at answering these questions. The first contribution is to avoid the discrete-time disconnected level sets by a decreasing sequence of bounded and connected sets that converges to the origin and that contain the future of the continuous-time trajectory. The second contribution deals with the joint stabilization of a sampled-data Lur’e system with non-uniform sampling. When the sampling period belongs to a finite set of values, this problem is reformulated as the joint stabilization of a discrete-time Lur’e switched system with norm-bounded uncertain parameters. Futhermore, if a quadratic criterion is associated with each mode, a min-switching strategy combined with LMI constraints allow to provide a solution to this problem. Finally the property of consistency for discrete-time switched Lur’e systems is investigated. It is shown that the min-switching strategy is consistent with respect to quadratic upper bounds of the performances. This result is applied on the stabilization of Lur’e systems with non-uniform sampling.
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Submitted on : Tuesday, September 1, 2015 - 6:13:33 PM
Last modification on : Saturday, October 8, 2022 - 12:03:11 PM
Long-term archiving on: : Wednesday, December 2, 2015 - 12:49:53 PM


  • HAL Id : tel-01191424, version 2



Julien Louis. Discrétisation des systèmes de Lur'e: stabilisation et consistance. Automatique / Robotique. Université de Lorraine, 2015. Français. ⟨NNT : 2015LORR0080⟩. ⟨tel-01191424v2⟩



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