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Extensions of Kharitonov Theorem to Positive Fractional Linear 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 asymptotic stability of interval positive continuous-time linear systems of integer and fractional orders is investigated. The classical Kharitonov theorem is extended to the interval positive continuous-time linear systems of integer and fractional orders. It is shown that:

  1. (1)

    The interval positive linear system is asymptotically stable if and only if the matrices bounding the state matrix are Hurwitz Metzler.

  2. (2)

    The interval positive fractional system is asymptotically stable if and only if bounding the state matrix are Hurwitz Metzler.

  3. (3)

    The interval positive of integer and fractional orders continuous-time linear systems with interval characteristic polynomials are asymptotically stable if and only if their lower bounds of the coefficients are positive.

It is shown that the interval positive fractional discrete-time linear systems are asymptotically stable if and only if the lower and upper bounds of the state matrices are asymptotically stable. The classical Kharitonov theorem is extended to the discrete-time interval positive fractional linear systems.

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Acknowledgement

This work was supported by National Science Centre in Poland under work No. 2017/27/B/ST7/02443.

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Authors and Affiliations

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

    Tadeusz Kaczorek

Authors
  1. Tadeusz Kaczorek
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Correspondence to Tadeusz Kaczorek .

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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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Kaczorek, T. (2020). Extensions of Kharitonov Theorem to Positive Fractional Linear 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_1

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