Relaxed stabilization criterion for T-S fuzzy systems by minimum-type piecewise-lyapunov-function-based switching fuzzy controller

Ying Jen Chen, Hiroshi Ohtake, Kazuo Tanaka, Wen June Wang, Hua O. Wang

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

This paper proposes the minimum-type piecewise-Lyapunov-function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie etal. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions as the Lyapunov function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov function as the Lyapunov function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.

Original languageEnglish
Article number6189778
Pages (from-to)1166-1173
Number of pages8
JournalIEEE Transactions on Fuzzy Systems
Volume20
Issue number6
DOIs
StatePublished - 2012

Keywords

  • Bilinear matrix inequality (BMI)
  • path-following method
  • piecewise Lyapunov function
  • relaxed stabilization criterion
  • switching fuzzy controller
  • Takagi-Sugeno (T-S) fuzzy system

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