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Error analysis for a class of numerical differentiator: application to state observation

Da-Yan Liu 1, 2 Olivier Gibaru 2, 3 Wilfrid Perruquetti 2, 4
2 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 : In this note, firstly a modified numerical differentiation scheme is presented. The obtained scheme is rooted in the numerical differentiation method of Mboup M., Join C., Fliess M. and uses the same algebraic approach based on operational calculus. Secondly an analysis of the error due to a corrupting noise in this estimation is conducted and some upper-bounds are given on this error. Lastly a convincing simulation example gives an estimation of the state variable of a nonlinear system where the measured output is noisy.
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https://hal.inria.fr/inria-00437129
Contributor : Dayan Liu <>
Submitted on : Sunday, November 29, 2009 - 3:17:14 PM
Last modification on : Friday, December 11, 2020 - 6:44:07 PM
Long-term archiving on: : Thursday, June 17, 2010 - 10:40:53 PM

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  • HAL Id : inria-00437129, version 1

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Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti. Error analysis for a class of numerical differentiator: application to state observation. 48th IEEE Conference on Decision and Control, Dec 2009, Shanghai, China. ⟨inria-00437129⟩

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