An analysis of approximation errors in calculation of the Grunwald-Letnikov fractional-order difference

• Autorzy: Kozioł, Kamil
• Języki publikacji: EN

Abstrakty

EN

This paper presents an analysis of approximation errors in calculation of fractional-order differences. The implementation of fractional-order difference is based on the well-known Grünwald-Letnikow notation. Simulation examples present the approximation precision depending on the fractional order and the summation limit.

• Czasopismo: Zeszyty Naukowe. Elektryka / Politechnika Opolska
• Rocznik: 2019
• Tom: z. 77
• Strony: 69--72
• Opis fizyczny: Bibliogr. 5 poz., rys.

Twórcy

autor

Kozioł, Kamil

• Faculty of Electrical Engineering, Automatic Control and Informatics Institute of Computer Science

Bibliografia

• [1] KACZOREK T.: Practical stability of positive fractional discrete-time linear systems. Bulletin of the Polish Academy of Sciences, Technical Sciences, Vol. 56, No. 4, pp. 313−317, doi: 10.2478/amcs-2018-0034, 2008
• [2] OSTALCZYK P.: Discrete Fractional Calculus. Applications in Control and Image Processing. Ser. in Computer Vision 4, World Scientific, doi.org/10.1142/9833, 2016
• [3] SIAMI M., TAVAZOEI M.S., HAERI M.: Stability preservation analysis in direct discretization of fractional order transfer functions. Signal Processing, Vol. 91, No. 3, pp. 508–512, doi: 10.1016/j.sigpro.2010.06.009, 2011
• [4] STANISŁAWSKI R., HUNEK W.P., LATAWIEC K.J.: Finite approximations of a discrete-time fractional derivative. in Proceedings of the 16th Interational Conference on Methods and Models in Automation and Robotics (MMAR ’11), pp. 142−145, Międzyzdroje, Poland, doi: 10.1109/MMAR.2011.6031333, 2011
• [5] STANISŁAWSKI R., RYDEL M., LATAWIEC K.J.: Modeling of discrete-time fractional- order state space systems using the balanced truncation method. Journal of the Franklin Institute, Vol. 354, No. 7, pp. 3008−3020, doi: 10.1016/ j.jfranklin.2017.02.003, 2017

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).