Membership-dependent stability conditions for type-1 and interval type-2 T–S fuzzy systems

Xiaozhan Yang*, Hak-Keung Lam, Ligang Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)
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This paper presents an idea to simplify and relax the stability conditions of Takagi–Sugeno (T–S) fuzzy systems based on the membership function extrema1. By considering the distribution of membership functions in a unified membership space, a graphical approach is provided to analyze the conservativeness of membership-dependent stability conditions. Membership function extrema are used to construct a simple and tighter convex polyhedron that encloses the membership trajectory and produces less conservative linear matrix inequality (LMI) conditions. The cases of both type-1 and interval type-2 T–S fuzzy systems are considered, and comparison with existing methods is made in the proposed membership vector framework.
Original languageEnglish
JournalFuzzy Sets and Systems
Early online date3 Feb 2018
Publication statusE-pub ahead of print - 3 Feb 2018


  • Stability analysis
  • T–S fuzzy system
  • Membership function
  • Convex polyhedron


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