Skip to Main content Skip to Navigation
Journal articles

Synthesis of fractional Laguerre basis for system approximation

Abstract : Fractional differentiation systems are characterized by the presence of non-exponential aperiodic multimodes. Although rational orthogonal bases can be used to model any $L_2[0, \infty[$ system, they fail to quickly capture the aperiodic multimode behavior with a limited number of terms. Hence, fractional orthogonal bases are expected to better approximate fractional models with fewer parameters. Intuitive reasoning could lead to simply extending the differentiation order of existing bases from integer to any positive real number. However, classical Laguerre, and by extension Kautz and generalized orthogonal basis functions, are divergent as soon as their differentiation order is non-integer. In this paper, the first fractional orthogonal basis is synthesized, extrapolating the definition of Laguerre functions to any fractional order derivative. Completeness of the new basis is demonstrated. Hence, a new class of fixed denominator models is provided for fractional system approximation and identification.
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00180684
Contributor : Rachid Malti <>
Submitted on : Saturday, October 20, 2007 - 11:09:08 AM
Last modification on : Tuesday, March 31, 2020 - 2:12:13 PM
Document(s) archivé(s) le : Sunday, April 11, 2010 - 11:24:01 PM

File

ThePaper.pdf
Files produced by the author(s)

Identifiers

Citation

Mohamed Aoun, Rachid Malti, François Levron, Alain Oustaloup. Synthesis of fractional Laguerre basis for system approximation. Automatica, Elsevier, 2007, 43 (9), pp.1640-1648. ⟨10.1016/j.automatica.2007.02.013⟩. ⟨hal-00180684⟩

Share

Metrics

Record views

380

Files downloads

885