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On Mikhailov Stability Conditions for a Class of Integer- and Commensurate Fractional-Order Discrete-Time Systems

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Advanced, Contemporary Control (PCC 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 708))

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Abstract

The Mikhailov stability condition is a classical stability test for continuous-time systems, similar to the well-known Nyquist method. However, in contrast to the Nyquist criterion, the Mikhailov stability tests do not reach considerable research attention. This paper introduces an extension of Mikhailov stability condition for two classes of a discrete-time system in terms of linear time-invariant system, and fractional-order one based on ‘forward-shifted’ Grünwald-Letnikov difference. Simulation experiments confirm the usefulness of the Mikhailov methods for stability analysis of discrete-time systems.

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Author information

Authors and Affiliations

  1. Department of Electrical, Control and Computer Engineering, Opole University of Technology, ul. Prószkowska 76, 45-758, Opole, Poland

    Rafał Stanisławski & Marek Rydel

Authors
  1. Rafał Stanisławski
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  2. Marek Rydel
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Corresponding author

Correspondence to Rafał Stanisławski .

Editor information

Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Marek Pawelczyk

  2. Silesian University of Technology, Gliwice, Poland

    Dariusz Bismor

  3. Silesian University of Technology, Gliwice, Poland

    Szymon Ogonowski

  4. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Janusz Kacprzyk

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Stanisławski, R., Rydel, M. (2023). On Mikhailov Stability Conditions for a Class of Integer- and Commensurate Fractional-Order Discrete-Time Systems. In: Pawelczyk, M., Bismor, D., Ogonowski, S., Kacprzyk, J. (eds) Advanced, Contemporary Control. PCC 2023. Lecture Notes in Networks and Systems, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-031-35170-9_2

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