AOUN, Mohamed; MALTI, Rachid; LEVRON, François; OUSTALOUP, Alain

doi:10.1016/j.automatica.2007.02.013

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

AOUN, Mohamed
Laboratoire de l'intégration, du matériau au système [IMS]

MALTI, Rachid
Laboratoire de l'intégration, du matériau au système [IMS]

LEVRON, François
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Automatica. 2007-09, vol. 43, n° 9, p. 1640-1648

Elsevier

Résumé en anglais

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.< Réduire

Mots clés en anglais

Orthonormal basis

fractional differentiation

Laguerre function

system approximation

identification

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Synthesis of fractional Laguerre basis for system approximation

Langue

Ce document a été publié dans

Résumé en anglais

Mots clés en anglais

URI

DOI

Origine

Unités de recherche