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Exponential Stability for a Class of Fractional Order Dynamic Systems

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

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Abstract

The paper presents a comparinson of exponential, Mittag-Leffler and generalized Mittag-Leffler stability problems for a class of fractional order dynamical systems. The considered system is described by state equation with diagonal state matrix, the spectrum of the system contains single, separated, real, decreasing eigenvalues. An example of such a system is a heat object described by a fractional order state equation. The fractional order derivative is described by Caputo and Caputo-Fabrizio operators. For the considered system the simple conditions of approximated equivalence of the all discussed stabilities are proposed. Results are illustrated by the numerical example.

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Acknowledgement

This paper was sponsored by AGH UST project no 11.11.120.817.

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Authors and Affiliations

  1. AGH University, al. A. Mickiewicza 30, 30059, Krakow, Poland

    Krzysztof Oprzędkiewicz & Wojciech Mitkowski

Authors
  1. Krzysztof Oprzędkiewicz
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  2. Wojciech Mitkowski
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Corresponding author

Correspondence to Krzysztof Oprzędkiewicz .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Oprzędkiewicz, K., Mitkowski, W. (2020). Exponential Stability for a Class of Fractional Order Dynamic Systems. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_13

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