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Investigation of Robust Stability for Fractional-Order LTI Systems with Multilinear Structure of Ellipsoidal Parametric Uncertainty

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Software Engineering Perspectives in Intelligent Systems (CoMeSySo 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1295))

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Abstract

The contribution focuses on the investigation of robust stability for fractional-order linear time-invariant (LTI) systems with the multilinear structure of ellipsoidal parametric uncertainty, i.e., the analyzed family of fractional-order polynomials has the multilinear uncertainty structure and an ellipsoid-shaped uncertainty bounding set. The robust stability test is based on the numerical calculation and subsequent plot of the value sets, and the application of the zero exclusion condition. Unlike the previously published works, this contribution shows that, contrary to the case of a two-dimensional ellipse of parameters, the internal points of a three-dimensional ellipsoid of parameters cannot create the boundary of the value set in the complex plane even under more complicated uncertainty structures, such as the multilinear one.

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Acknowledgments

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme project No. LO1303 (MSMT-7778/2014).

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Authors and Affiliations

  1. Centre for Security, Information and Advanced Technologies (CEBIA–Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, nám. T. G. Masaryka 5555, 760 01, Zlín, Czech Republic

    Radek Matušů

  2. Department of Computer Engineering, Faculty of Engineering, Inonu University, 44280, Malatya, Turkey

    Bilal Şenol

Authors
  1. Radek Matušů
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  2. Bilal Şenol
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Corresponding author

Correspondence to Radek Matušů .

Editor information

Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Petr Silhavy

  3. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Zdenka Prokopova

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Matušů, R., Şenol, B. (2020). Investigation of Robust Stability for Fractional-Order LTI Systems with Multilinear Structure of Ellipsoidal Parametric Uncertainty. In: Silhavy, R., Silhavy, P., Prokopova, Z. (eds) Software Engineering Perspectives in Intelligent Systems. CoMeSySo 2020. Advances in Intelligent Systems and Computing, vol 1295. Springer, Cham. https://doi.org/10.1007/978-3-030-63319-6_39

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