l-based stability criteria and its applications on FLC systems

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

1 Scopus Citations
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Author(s)

  • D. Z. Liao
  • L. F. Yeung

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)35-57
Journal / PublicationFuzzy Sets and Systems
Volume139
Issue number1
Publication statusPublished - 1 Oct 2003

Abstract

In this paper, a new stability analysis and design method for the fuzzy logical systems described by the Takagi-Sugeno model is proposed. The proposed fuzzy controller is implemented by a parallel distributed compensation structure. The closed-loop system can be expressed as a linear time-variant system. A minimum transition matrix set can be determined by the fuzzy rule structure, so that it contains the transition matrices of the closed-loop system. Thus the stability of the system defined over the set is sufficient to ensure the stability of the closed-loop system. A common l Lyapunov function method is employed for the stability analysis of the system defined over the transition matrix set. It is proved that the existence of the l Lyapunov function is the sufficient and necessary stability condition of the system defined over the transition matrix set. Thus the l Lyapunov function can be applied to more cases than quadratic Lyapunov functions. A convenient stability criterion based on l Lyapunov function is also given in this paper. By using geometric properties of l Lyapunov functions, an iterative algorithm is introduced to construct the required l Lyapunov function. © 2002 Elsevier B.V. All rights reserved.

Research Area(s)

  • Control theory, Fuzzy system, Lyapunov function, Parallel distributed compensation, Stability analysis, Variable structure

Citation Format(s)

l-based stability criteria and its applications on FLC systems. / Liao, D. Z.; Yeung, L. F.
In: Fuzzy Sets and Systems, Vol. 139, No. 1, 01.10.2003, p. 35-57.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review