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Stabilization of Lebesgue's sampled systems with bounded controls: the chain of integrators case

Nicolas Marchand 1, 2
1 NECS [2007-2015] - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA [2007-2015] - Département Automatique
2 GIPSA-SYSCO [2007-2015] - GIPSA - Systèmes non linéaires et complexité
GIPSA-DA [2007-2015] - Département Automatique
Abstract : In this paper, the stabilization of a chain of integrators in the Lebesgue sampling context is considered. Lebesgue sampling refers to a sampling scheme where measurements are not taken at periodic instants but when variables crosse a priori defined levels. The paper proposes a nonlinear control law that stabilizes the system in the sense that it renders asymptotically stable any a priori given hyper-rectangle strictly larger and encompassing the smallest set where the states fail to be detectable because of the quantization precision. The control law is a sum of saturated linear feedback computed with quantized measurements.
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Nicolas Marchand. Stabilization of Lebesgue's sampled systems with bounded controls: the chain of integrators case. 17th IFAC World Congress (IFAC WC 2008), Jul 2008, Seoul, South Korea. ⟨10.3182/20080706-5-KR-1001.2874⟩. ⟨hal-00200591⟩

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