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

  • Radek MatušůEmail author
  • Bilal Şenol
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1295)


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.


Robust stability Fractional-order systems Ellipsoidal parametric uncertainty Multilinear uncertainty Value set 



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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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Centre for Security, Information and Advanced Technologies (CEBIA–Tech), Faculty of Applied InformaticsTomas Bata University in ZlínZlínCzech Republic
  2. 2.Department of Computer Engineering, Faculty of EngineeringInonu UniversityMalatyaTurkey

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