Improved cubic negative determination for T-S fuzzy system with time-varying delay

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-07-17 DOI:10.1016/j.fss.2025.109539

Han Xue, Yuanyuan Zhang, Xinzuo Ma, Seakweng Vong

引用次数: 0

Abstract

This paper investigates the stability analysis of Takagi-Sugeno (T-S) fuzzy control systems with time-varying delays. To leverage the interaction between fuzzy rules and system states in T-S fuzzy models, two enhanced line-integral type Lyapunov-Krasovskii functionals (LKFs) are constructed along distinct integral paths. Furthermore, an improved negative-determination lemma for cubic polynomials is developed, offering more relaxed negative-determination conditions and enabling less conservative stability criteria for the LKF derivative. The stability conditions, which are delay-dependent, are formulated as linear matrix inequalities (LMIs). To demonstrate the advantages and effectiveness of the proposed method, numerical examples are provided, showcasing improved performance compared to existing approaches.

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时变时滞T-S模糊系统的改进三次负确定

本文研究了具有时变时滞的Takagi-Sugeno （T-S）模糊控制系统的稳定性分析。为了利用T-S模糊模型中模糊规则和系统状态之间的相互作用，沿着不同的积分路径构造了两个增强的线积分型Lyapunov-Krasovskii泛函（lkf）。此外，提出了一种改进的三次多项式的负决定引理，为LKF导数提供了更宽松的负决定条件和更少保守的稳定性判据。将时滞相关的稳定性条件表述为线性矩阵不等式（lmi）。为了证明该方法的优点和有效性，给出了数值算例，与现有方法相比，性能得到了改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.