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Paper details
Number 4 - December 2012
Volume 22 - 2012
Normalized finite fractional differences: Computational and accuracy breakthroughs
Rafał Stanisławski, Krzysztof J. Latawiec
Abstract
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.
Keywords
fractional difference, Grünwald–Letnikov difference, stability analysis, recursive computation, adaptive systems