Robust stability of fractional order polynomials with complicated uncertainty structure

PLoS One. 2017 Jun 29;12(6):e0180274. doi: 10.1371/journal.pone.0180274. eCollection 2017.

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.

MeSH terms

  • Algorithms
  • Models, Theoretical*
  • Uncertainty*

Grants and funding

This work was supported by the European Regional Development Fund under the project CEBIA‐Tech Instrumentation No. CZ.1.05/2.1.00/19.0376 and by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme project No. LO1303 (MSMT‐7778/2014). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.