research-article

On the local quadratic stability of T–S fuzzy systems in the vicinity of the origin

Authors:

Do Wan KimAuthors Info & Claims

Volume 497, Issue C

https://doi.org/10.1016/j.fss.2024.109113

Published: 01 December 2024 Publication History

Abstract

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. Discussions on the inherent limitations associated with fuzzy Lyapunov approaches are also given. To illustrate the theoretical results, we provide comprehensive examples that demonstrate the core concepts and validate the efficacy of the proposed conditions.

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Index Terms

On the local quadratic stability of T–S fuzzy systems in the vicinity of the origin
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Probabilistic reasoning
      2. Vagueness and fuzzy logic
  2. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Fuzzy Sets and Systems

Fuzzy Sets and Systems Volume 497, Issue C

Dec 2024

120 pages

Issue’s Table of Contents

Elsevier B.V.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 December 2024

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