A New Design of Membership-Function-Dependent Controller for T-S Fuzzy Systems Under Imperfect Premise Matching

Changzhu Zhang, Hak Keung Lam, Jianbin Qiu, Chengju Liu, Qijun Chen

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)
280 Downloads (Pure)

Abstract

This paper is concerned with the problem of membership-function-dependent controller design for a class of discrete-time T-S fuzzy systems. Based on the partition method of premise variable space, the original T-S fuzzy model is equivalently converted into a kind of piecewise-fuzzy system. Then by employing some staircase functions, the continuous membership functions are approximated by a series of discrete values, via which the information of membership functions is brought into the stability analysis to reduce the design conservatism. With piecewise Lyapunov functions, the approaches to the piecewise-fuzzy state feedback and observer-based output feedback controller design are proposed, respectively, in terms of linear matrix inequalities such that the closed-loop system is asymptotically stable with a prescribed <formula><tex>$\mathcal{H}_{\infty}$</tex></formula> performance level. It is shown that the membership functions of the fuzzy model and fuzzy controllers are not necessarily the same, which allows more design flexibility. Finally, two illustrative examples are provided to show the effectiveness of the developed methods.

Original languageEnglish
JournalIEEE Transactions on Fuzzy Systems
Early online date9 Nov 2018
DOIs
Publication statusE-pub ahead of print - 9 Nov 2018

Keywords

  • Analytical models
  • controller design
  • Fuzzy systems
  • imperfect premise matching
  • Linear matrix inequalities
  • Lyapounv stability
  • Lyapunov methods
  • membershipfunction-dependent
  • Stability analysis
  • State feedback
  • Symmetric matrices
  • Takagi-Sugeno fuzzy systems

Fingerprint

Dive into the research topics of 'A New Design of Membership-Function-Dependent Controller for T-S Fuzzy Systems Under Imperfect Premise Matching'. Together they form a unique fingerprint.

Cite this