Linear systems with unstructured multiplicative uncertainty: Modeling and robust stability analysis

PLoS One. 2017 Jul 12;12(7):e0181078. doi: 10.1371/journal.pone.0181078. eCollection 2017.

Abstract

This article deals with continuous-time Linear Time-Invariant (LTI) Single-Input Single-Output (SISO) systems affected by unstructured multiplicative uncertainty. More specifically, its aim is to present an approach to the construction of uncertain models based on the appropriate selection of a nominal system and a weight function and to apply the fundamentals of robust stability investigation for considered sort of systems. The initial theoretical parts are followed by three extensive illustrative examples in which the first order time-delay, second order and third order plants with parametric uncertainty are modeled as systems with unstructured multiplicative uncertainty and subsequently, the robust stability of selected feedback loops containing constructed models and chosen controllers is analyzed and obtained results are discussed.

MeSH terms

  • Programming, Linear*
  • 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.