Application of Value Set Concept to Ellipsoidal Polynomial Families with Multilinear Uncertainty Structure

  • Radek MatušůEmail author
  • Bilal Şenol
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1047)


The contribution intends to present the application of the value set concept to the ellipsoidal polynomial families with multilinear uncertainty structure. It is a follow-up to the previously published work, where the ellipsoidal polynomial families with affine linear uncertainty structure were studied. In the first parts of this paper, the basic terms related to the robustness under parametric uncertainty (e.g., uncertainty structure, uncertainty bounding set, family, and value set) are briefly recalled, with the accent on the ellipsoidal polynomial families. Subsequently, the non-convex value sets of the illustrative ellipsoidal polynomial family with multilinear uncertainty structure are plotted and analyzed. It is shown that the boundaries of the value set need not to mapped only from the boundaries in the parameter space but possibly also from the internal points.


Value set Ellipsoidal uncertainty Spherical uncertainty Family of polynomials Multilinear uncertainty 



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) and also by the European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089. This assistance is very gratefully acknowledged.


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© Springer Nature Switzerland AG 2019

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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