Non-asymptotic fractional order differentiators via an algebraic parametric method

Da-Yan Liu 1 Olivier Gibaru 2, 3 Wilfrid Perruquetti 2, 4
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations.
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https://hal.inria.fr/hal-00713338
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Submitted on : Saturday, June 30, 2012 - 1:33:04 PM
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  • HAL Id : hal-00713338, version 1
  • ARXIV : 1207.0129

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Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti. Non-asymptotic fractional order differentiators via an algebraic parametric method. 1st International Conference on Systems and Computer Science, Aug 2012, Villeneuve d'ascq, France. ⟨hal-00713338⟩

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