Relaxed stability conditions for the Takagi-Sugeno fuzzy system using a polynomial non-quadratic Lyapunov function

Han Sol Kim, Jin Bae Park, Young Hoon Joo

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this study, sum-of-squares (SOS)-based relaxed stability conditions for the continuous-time Takagi-Sugeno (T-S) fuzzy system are derived using a polynomial non-quadratic Lyapunov function (PNQLF). The proposed methods consist of two approaches. Like the previous studies, the first uses the upper bounds on a time derivative of the fuzzy weighting function (TDFWF), and the other directly uses the TDFWF in order to obtain relaxed results and enlarge the domain of attraction. Moreover, unlike the conventional non-quadratic Lyapunov function, the newly proposed PNQLF uses different fuzzy weighting functions from those of the system in order to solve the existing problems. Finally, the effectiveness of the proposed methods is demonstrated by some numerical examples.

Original languageEnglish
Pages (from-to)1590-1599
Number of pages10
JournalIET Control Theory and Applications
Volume10
Issue number13
DOIs
Publication statusPublished - 2016 Aug 29

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Takagi-Sugeno Fuzzy Systems
Fuzzy Function
Weighting Function
Fuzzy systems
Lyapunov functions
Stability Condition
Lyapunov Function
Polynomials
Polynomial
Derivatives
Derivative
Domain of Attraction
Sum of squares
Continuous Time
Upper bound
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Control and Optimization
  • Electrical and Electronic Engineering

Cite this

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Relaxed stability conditions for the Takagi-Sugeno fuzzy system using a polynomial non-quadratic Lyapunov function. / Kim, Han Sol; Park, Jin Bae; Joo, Young Hoon.

In: IET Control Theory and Applications, Vol. 10, No. 13, 29.08.2016, p. 1590-1599.

Research output: Contribution to journalArticle

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