Abstract
The problem of the stability of the Grünwald–Letnikov–type linear discrete-time systems with fractional positive orders is studied. The method of reducing the considered systems by transforming them to the multi-order linear systems with the partial orders from the interval (0, 1] is presented. For the reduced multi-order systems the conditions for the stability are formulated based on the \(\mathcal {Z}\)-transform as an effective method for stability analysis of linear systems.
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Acknowledgments
The project was supported by the founds of National Science Centre granted on the bases of the decision number DEC-2011/03/B/ST7/03476. The work was supported by Bialystok University of Technology grant G/WM/3/2012.
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Wyrwas, M., Mozyrska, D. (2016). Stability of Linear Discrete–Time Systems with Fractional Positive Orders. In: Domek, S., Dworak, P. (eds) Theoretical Developments and Applications of Non-Integer Order Systems. Lecture Notes in Electrical Engineering, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-23039-9_13
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DOI: https://doi.org/10.1007/978-3-319-23039-9_13
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