More relaxed stability analysis and positivity analysis for positive polynomial fuzzy systems via membership functions dependent method

Meng Han, H. K. Lam*, Fucai Liu, Yinggan Tang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
105 Downloads (Pure)

Abstract

In this paper, the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy-model-based (PPFMB) control system are studied. Also, in order to improve the flexibility of controller design, a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed. In the existing literatures, it is proved that the LCLF can reduce the conservatism of stability results. However, the LCLF generally results in non-convex conditions which is still a conservatism source. To handle the non-convex conditions, the sector nonlinear concept is applied to handle non-convex terms in stability conditions, and the obstacles caused by mismatched membership functions can be eliminated by PLMF dependent method. In addition, to relax the conservatism caused by the lack of membership functions information, the PLMF dependent positivity analysis are performed for the first time. Meanwhile, PLMF dependent method is extended to stability conditions to obtained more relaxed conditions. Finally, a simulation example is presented to verify the feasibility of this method.

Original languageEnglish
Pages (from-to)111-131
Number of pages21
JournalFuzzy Sets and Systems
Volume432
Early online date11 Feb 2022
DOIs
Publication statusPublished - 28 Mar 2022

Keywords

  • Linear copositive Lyapunov function (LCLF)
  • Piecewise linear membership functions (PLMF) dependent method
  • Positive polynomial fuzzy-model-based (PPFMB) control systems
  • Sector nonlinear concept

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