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Improved stability conditions for sampled data systems with jitter

Laurentiu Hetel 1, * Alexandre Kruszewski 1 Thierry-Marie Guerra 2 Jean-Pierre Richard 3, 4
* Corresponding author
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : This paper is concerned with the discrete time approach for the robust stability of sampled-data systems (Astrom and Wittenmark 1997) with sampling jitter. We assume that the sampling is unknown, time-varying and bounded in a given interval. Several discrete-timea pproaches exist in the literature. The intention of the paper is to clearly analyse the relations between them and to indicate the sources of conservatism. It will point out that the different existing models can be studied in the framework of difference inclusions with polytopic and norm bounded components. Furthermore, it will show how to reduce the conservatisms by using recent stability analysis tools based on Lyapunov functions with non-monotonic Lyapunov increment. The idea is to improve the stability conditions by considering α-samples variations, i.e. $V (x_{k+α}) − V (x_{k}) < 0$. Numerical examples illustrate the effectiveness of the approach.
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Contributor : Jean-Pierre Richard <>
Submitted on : Wednesday, September 23, 2009 - 5:16:44 PM
Last modification on : Friday, March 26, 2021 - 10:59:08 AM


  • HAL Id : inria-00419438, version 1


Laurentiu Hetel, Alexandre Kruszewski, Thierry-Marie Guerra, Jean-Pierre Richard. Improved stability conditions for sampled data systems with jitter. ROCOND'09, 6th IFAC Symposium on Robust Control Design, Jun 2009, Haifa, Israel. ⟨inria-00419438⟩



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