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About the Lyapunov exponent of sampled-data systems with non-uniform sampling

Laurentiu Hetel 1 Alexandre Kruszewski 1 Jean-Pierre Richard 2, 3 
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Centrale Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
3 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : In this paper we propose a method for evaluating the Lyapunov exponent of sampled-data systems with sampling jitter. We consider the case of systems in which the sampling interval is unknown, time-varying and bounded in a given interval. In order to take into account the inter-sampling behaviour of the system, the problem is addressed from the continuous time point of view. The approach exploits the fact that the command is a piecewise constant signal and leads to less conservative stability conditions. Using geometrical arguments, a lower bound of the Lyapunov exponent can be expressed as a generalized eigenvalue problem. Numerical examples are given to illustrate the approach.
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https://hal.inria.fr/inria-00419444
Contributor : Jean-Pierre Richard Connect in order to contact the contributor
Submitted on : Wednesday, September 23, 2009 - 5:37:16 PM
Last modification on : Wednesday, March 23, 2022 - 3:51:21 PM

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  • HAL Id : inria-00419444, version 1

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Laurentiu Hetel, Alexandre Kruszewski, Jean-Pierre Richard. About the Lyapunov exponent of sampled-data systems with non-uniform sampling. TDS'09, 8th IFAC Workshop on Time Delay Systems, Sep 2009, Sinaia, Romania. ⟨inria-00419444⟩

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