Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1128.93019
Aoun, M.; Malti, R.; Levron, F.; Oustaloup, A.
Synthesis of fractional Laguerre basis for system approximation.
(English)
[J] Automatica 43, No. 9, 1640-1648 (2007). ISSN 0005-1098

Summary: 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.
MSC 2000:
*93B50 Synthesis problems
93B30 System identification
26A33 Fractional derivatives and integrals (real functions)
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: orthonormal basis; fractional differentiation; Laguerre function; system approximation; identification

Highlights
Master Server