A new approach to stability and stabilization analysis for continuous-time Takagi-Sugeno fuzzy systems with time delay

Likui Wang, Hak Keung Lam

Research output: Contribution to journalArticlepeer-review

172 Citations (Scopus)
527 Downloads (Pure)

Abstract

Till now, there are lots of stability and stabilization results about T-S (Takagi-Sugeno) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov-Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T-S fuzzy systems with time delay. Different from the existing results in the literature, the integrand of the Lyapunov-Krasovskii functional in this paper depends not only on the integral variable but also on the membership functions, and thus, the information of the time-derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds. Utilizing the information of the time-derivative of membership, a bunch of controllers are designed according to their sign, and then a switching idea is applied to stabilize the fuzzy system. In the end, two examples are given to illustrate the feasibility and validity of the design and analysis.

Original languageEnglish
Number of pages6
JournalIEEE Transactions on Fuzzy Systems
Issue number99
Early online date14 Sept 2017
DOIs
Publication statusE-pub ahead of print - 14 Sept 2017

Keywords

  • Membership dependent Lyapunov-Krasovskii function
  • Parallel distributed compensation law
  • Takagi-Sugenos fuzzy model
  • Time delay

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