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Stability Conditions for the New Model of Fractional Discrete-Time Linear Scalar Systems with One Delay

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Automation 2018 (AUTOMATION 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 743))

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Abstract

In the paper graphical and analytical methods for stability analysis are given for the fractional discrete-time linear scalar systems with one delay described by the new model. The classical D-partition method is used to stability analysis. The practical stability and the asymptotic stability are considered.

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References

  1. Ackermann, J.: Sampled-Data Control Systems. Springer, Berlin (1985)

    Book  MATH  Google Scholar 

  2. Busłowicz, M.: Stability of fractional discrete-time linear scalar systems with one delay. Pomiary Automatyka Robotyka 2, 7 (2013)

    Google Scholar 

  3. Busłowicz, M.: Stability conditions for linear continuous-time fractional-order state-delayed systems. Bull. Polish Acad. Sci. Techn. Sci. 64, 3–7 (2016)

    Google Scholar 

  4. Busłowicz, M., Kaczorek, T.: Simple conditions for practical stability of linear positive fractional discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 19, 263–269 (2009)

    MathSciNet  MATH  Google Scholar 

  5. Busłowicz, M., Ruszewski, A.: Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems. Bull. Polish Acad. Sci. Techn. Sci. 61, 779–786 (2013)

    Google Scholar 

  6. Dzieliński, A., Sierociuk, D.: Stability of discrete fractional state-space systems. J. Vibr. Control 14, 1543–1556 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gryazina, E.N., Polyak, B.T., Tremba, A.A.: D-decomposition technique state-of-the-art. Autom. Remote Control 69(12), 1991–2026 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kaczorek, T.: Practical stability of positive fractional discrete-time systems. Bull. Polish Acad. Sci. Techn. Sci. 56, 313–317 (2008)

    Google Scholar 

  9. Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  10. Kaczorek, T.: A new approach to the realization problem for fractional discrete-time linear systems. Bull. Polish Acad. Sci. 64, 9–14 (2016)

    Google Scholar 

  11. Kaczorek, T., Ostalczyk, P.: Responses comparison of the two discrete-time linear fractional state-space models. Fractional Calculus Appl. Anal. 19, 789–805 (2016)

    MathSciNet  MATH  Google Scholar 

  12. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)

    MATH  Google Scholar 

  13. Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-Order Systems and Controls. Springer, London (2010)

    Book  MATH  Google Scholar 

  14. Ostalczyk, P.: Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains. Int. J. Appl. Math. Comput. Sci. 22, 533–538 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ostalczyk, P.: Discrete Fractional Calculus: Applications in Control and Image Processing. Series in Computer Vision. World Scientific Publishing, Singapore (2016)

    Book  MATH  Google Scholar 

  16. Ruszewski, R.: Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model. Arch. Control Sci. 17, 340–344 (2016)

    Google Scholar 

  17. Ruszewski, A.: 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. LNEE, vol. 407, pp. 381–389. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45474-0_34

    Chapter  Google Scholar 

  18. Ruszewski, R., Busłowicz, M.: Practical and asymptotic stability of fractional discrete-time scalar systems with multiple delays. In: Malinowski, K., et al. (eds.) Recent Advances in Control and Automation, pp. 183–192. Academic Publishing House Exit, Warsaw (2014)

    Google Scholar 

  19. Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering. Springer, London (2007)

    MATH  Google Scholar 

  20. Stanisławski, R., Latawiec, K.J.: Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: new necessary and sufficient conditions for asymptotic stability. Bull. Polish Acad. Sci. 61, 353–361 (2013)

    Google Scholar 

  21. Stanisławski, R.: New results in stability analysis for LTI SISO systems modeled by GL-discretized fractional-order transfer functions. Fractional Calc. Appl. Anal. 20, 243–259 (2017)

    MathSciNet  MATH  Google Scholar 

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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. (2018). Stability Conditions for the New Model of Fractional Discrete-Time Linear Scalar Systems with One Delay. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2018. AUTOMATION 2018. Advances in Intelligent Systems and Computing, vol 743. Springer, Cham. https://doi.org/10.1007/978-3-319-77179-3_35

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  • DOI: https://doi.org/10.1007/978-3-319-77179-3_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77178-6

  • Online ISBN: 978-3-319-77179-3

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