Normalized finite fractional differences: Computational and accuracy breakthroughs

Stanisławski, R. ; Latawiec, K. J.

International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 4, pp. 907-919.

Résumé

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.

Détail

Keywords: fractional difference, Grünwald-Letnikov difference, stability analysis, recursive computation, adaptive systems
Mots-clés : różnica ułamkowa, różnica Grünwalda-Letnikowa, analiza stabilności, system adaptacyjny

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