Reachability Analysis-Based Interval Estimation for Discrete-Time Takagi-Sugeno Fuzzy Systems

Shenghui Guo, Weijie Ren, Choon Ki Ahn, Chenglin Wen, Hak Keung Lam

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Considering disturbances, noise, and sensor faults, this article investigates interval estimation for discrete-time Takagi-Sugeno fuzzy systems. To obtain precise estimation results and attenuate disturbances and noise in the system simultaneously, we integrate robust observers based on the H∞ technique and reachability analysis. Two novel observer gain computation methods are proposed for different purposes. The time-invariant method relaxes the original design conditions by transforming the parameterized linear matrix inequality (LMI) into a series of LMIs to increase computational speed, while the time-varying method employs the parameterized LMI directly and conducts calculation online. Furthermore, reachable set representations for error dynamics are formulated by making use of both time-invariant observer gain and time-varying observer gain. An inverted pendulum system simulation and a comparative numerical simulation are studied to illustrate the effectiveness and superiority of the developed methods.

Original languageEnglish
Pages (from-to)1981-1992
Number of pages12
JournalIEEE Transactions on Fuzzy Systems
Issue number6
Publication statusPublished - 2022 Jun 1

Bibliographical note

Publisher Copyright:
© 1993-2012 IEEE.


  • Discrete-time systems
  • Takagi-Sugeno fuzzy systems
  • interval estimation
  • parameterized linear matrix inequality (LMI)
  • reachability analysis
  • robust observer

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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