Output feedback control synthesis and stabilization for positive polynomial fuzzy systems under L1 performance

Aiwen Meng*, Hak Keung Lam, Fucai Liu, Ziguang Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

1 Citation (Scopus)
60 Downloads (Pure)

Abstract

This paper presents the stabilization for positive nonlinear systems using polynomial fuzzy models. To conform better to the practical scenarios that system states are not completely measurable, the static output feedback (SOF) control strategy instead of the state feedback control method is employed to realize the stability and positivity of the positive polynomial fuzzy system (PPFS) with satisfying L1-induced performance. However, some troublesome problems in analysis and control design will follow, such as the non-convex problem. Fortunately, by doing mathematical tricks, the non-convex problem is skillfully dealt with. Furthermore, the neglect of external disturbances may lead to a great negative impact on the performance of positive systems. For the sake of guaranteeing the asymptotic stability and positivity under the satisfaction of the optimal performance of the PPFS, it is significant to take the L1-induced performance requirement into consideration as well. In addition, a linear co-positive Lyapunov function is chosen so that the positivity can be extracted well and the stability analysis becomes simple. By using the sum of squares (SOS) technique, the convex stability and positivity conditions in the form of SOS are derived. Eventually, for illustrating the advantages of the proposed method, a simulation example is shown in the simulation section.

Original languageEnglish
Title of host publicationFrontiers in Artificial Intelligence and Applications
EditorsAntonio J. Tallon-Ballesteros
PublisherIOS Press BV
Pages135-145
Number of pages11
ISBN (Electronic)9781643681344
DOIs
Publication statusPublished - 2020
Event6th International Conference on Fuzzy Systems and Data Mining, FSDM 2020 - Virtual, Online, China
Duration: 13 Nov 202016 Nov 2020

Publication series

NameFrontiers in Artificial Intelligence and Applications
Volume331
ISSN (Print)0922-6389

Conference

Conference6th International Conference on Fuzzy Systems and Data Mining, FSDM 2020
Country/TerritoryChina
CityVirtual, Online
Period13/11/202016/11/2020

Keywords

  • L1 performance
  • positive polynomial fuzzy system (PPFS)
  • stability analysis
  • static output feedback (SOF)
  • sum of squares (SOS)

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