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Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

Abstract

In the paper the problem of asymptotic stability of fractional discrete-time linear systems described by the new model are addressed. Necessary and sufficient conditions for asymptotic stability are established. It is shown that location of all eigenvalues of the state matrix in the stability region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. The considerations are illustrated by numerical examples.

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Acknowledgments

This work was supported by the National Science Centre in Poland under the work No. 2014/13/B/ST7/03467.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351, Białystok, Poland

    Andrzej Ruszewski

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  1. Andrzej Ruszewski
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Correspondence to Andrzej Ruszewski .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Ruszewski, A. (2017). Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_34

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

  • eBook Packages: EngineeringEngineering (R0)

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