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Robust stability of fractional order polynomials with complicated uncertainty structure

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  • Radek Matušů
  • Bilal Şenol
  • Libor Pekař

Abstract

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition.

Suggested Citation

  • Radek Matušů & Bilal Şenol & Libor Pekař, 2017. "Robust stability of fractional order polynomials with complicated uncertainty structure," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-13, June.
    • Handle: RePEc:plo:pone00:0180274
    DOI: 10.1371/journal.pone.0180274
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    References listed on IDEAS

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    1. Yin, Chun & Zhong, Shou-ming & Huang, Xuegang & Cheng, Yuhua, 2015. "Robust stability analysis of fractional-order uncertain singular nonlinear system with external disturbance," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 351-362.
    2. Chang, Xiao-Heng & Xiong, Jun & Park, Ju H., 2016. "Fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 213-225.
    3. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
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