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On explicit stability conditions for a linear fractional difference system

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Abstract

The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1,..., with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples.

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Authors and Affiliations

  1. Institute of Mathematics, Brno University of Technology, Technická 2, CZ-616 69, Brno, Czech Republic

    Jan Čermák

  2. Department of Mathematics, University of Pannonia Pf 158, Egyetem u. 10, H-8201, Veszprém, Hungary

    István Győri

  3. Institute of Mathematics, Brno University of Technology Technická 2, CZ-616 69, Brno, Czech Republic

    Ludĕk Nechvátal

Authors
  1. Jan Čermák
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  2. István Győri
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  3. Ludĕk Nechvátal
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Correspondence to Jan Čermák.

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Čermák, J., Győri, I. & Nechvátal, L. On explicit stability conditions for a linear fractional difference system. FCAA 18, 651–672 (2015). https://doi.org/10.1515/fca-2015-0040

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  • DOI: https://doi.org/10.1515/fca-2015-0040

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