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Robust Stability of a Class of an Uncertain Fractional Discrete-Time Linear State-Space System

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Automation 2017 (ICA 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 550))

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Abstract

This paper presents the problems of robust asymptotic stability of fractional-order discrete-time linear systems with uncertainty. It is assumed that the system matrix is the interval matrix and the fractional order \(\alpha \) satisfies \(0< \alpha < 1\). The new robust stability conditions are given based on the matrix measure and Gershgorin’s theorem for the interval matrices. The considerations are illustrated by numerical examples.

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Acknowledgement

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 .

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Editors and Affiliations

  1. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Roman Szewczyk

  2. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Cezary Zieliński

  3. Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Małgorzata Kaliczyńska

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Ruszewski, A. (2017). Robust Stability of a Class of an Uncertain Fractional Discrete-Time Linear State-Space System. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2017. ICA 2017. Advances in Intelligent Systems and Computing, vol 550. Springer, Cham. https://doi.org/10.1007/978-3-319-54042-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-54042-9_18

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  • Online ISBN: 978-3-319-54042-9

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