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Analysis of the Positivity and Stability of Fractional Discrete-Time Nonlinear Systems

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Positive Systems (POSTA 2016)

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 471))

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Abstract

The positivity and asymptotic stability of the discrete-time nonlinear systems are addressed. Necessary and sufficient conditions for the positivity and sufficient conditions for the asymptotic stability of the nonlinear systems are established. The proposed stability tests are based on an extension of the Lyapunov method to the positive nonlinear systems. The effectiveness of the tests are demonstrated on examples.

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Acknowledgements

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

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Bialystok University of Technology, Bialystok, Poland

    Tadeusz Kaczorek

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  1. Tadeusz Kaczorek
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Correspondence to Tadeusz Kaczorek .

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Editors and Affiliations

  1. Università Campus Biomedico , Rome, Italy

    Filippo Cacace

  2. Sapienza Università di Roma , Rome, Italy

    Lorenzo Farina

  3. Università Campus Biomedico , Rome, Italy

    Roberto Setola

  4. Università dell’Aquila , L'Aquila, Italy

    Alfredo Germani

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Kaczorek, T. (2017). Analysis of the Positivity and Stability of Fractional Discrete-Time Nonlinear Systems. In: Cacace, F., Farina, L., Setola, R., Germani, A. (eds) Positive Systems . POSTA 2016. Lecture Notes in Control and Information Sciences, vol 471. Springer, Cham. https://doi.org/10.1007/978-3-319-54211-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-54211-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54210-2

  • Online ISBN: 978-3-319-54211-9

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