Implementation of fractional-order difference via Takenaka-Malmquist functions

Rafał Stanisławski, Kamil Kozioł and Marek Rydel

Applied Mathematics and Computation, 2022, vol. 434, issue C

Abstract: The paper presents a new definition of nabla fractional-order difference, equivalent to the Grünwald-Letnikov difference. The difference is based on the general approach of orthonormal basis functions in terms of discrete-time Takenaka-Malmquist filters. The main advantage of the proposed definition is that for finite model length, the model quickly converges to the actual difference. The paper proposes the method of selecting the poles of the Takenaka-Malmquist functions. It also proposes the implementation of the Takenaka-Malmquist-based difference in non-commensurate state-space system and fractional-order integrator. Simulation experiments show the proposed methodology’s high effectiveness in modeling fractional-order difference, integrator, and non-commensurate state-space systems.

Keywords: Nabla discrete-time difference; Grünwald-Letnikov difference; Takenaka-Malmquist functions; Non-commensurate fractional-order state-space system (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322005264

DOI: 10.1016/j.amc.2022.127452

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