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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00713338, version 1 |
| arXiv: 1207.0129 |
| See detailed view |  BibTeX,EndNote,... |
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| 1st International Conference on Systems and Computer Science, Villeneuve d'ascq : France (2012) |
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| Non-asymptotic fractional order differentiators via an algebraic parametric method |
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| Da-Yan Liu 1Olivier Gibaru 2, 3 |
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| (2012-08-29) |
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| 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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| 1: | Estimation Modelling and ANalysis Group (KAUST-MCSE) |
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King Abdullah University of Science and Technology |
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| 2: | Non-A (INRIA Lille - Nord Europe) |
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INRIA : LILLE - NORD EUROPE |
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| 3: | Laboratoire des Sciences de l'Information et des Systèmes (LSIS) |
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CNRS : UMR6168 – Arts et Métiers ParisTech – Université Paul Cézanne - Aix-Marseille III – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I – Université Sud Toulon Var |
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| 4: | Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS) |
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CNRS : UMR8219 – Université Lille I - Sciences et technologies – Ecole Centrale de Lille |
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| LAGIS-SYNER |
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| Domain | : | Mathematics/Numerical Analysis Computer Science/Signal and Image Processing Engineering Sciences/Signal and Image processing |
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| Attached file list to this document: | ||||||||||
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| hal-00713338, version 1 | |
| http://hal.inria.fr/hal-00713338 | |
| oai:hal.inria.fr:hal-00713338 | |
| From: Da-Yan Liu | |
| Submitted on: Saturday, 30 June 2012 13:33:04 | |
| Updated on: Wednesday, 19 September 2012 14:44:34 | |
