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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (4): 645-656.doi: 10.3969/j.issn.1005-3085.2025.04.004cstr: 32411.14.cjem.CN61-1269/O1.2025.04.004

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改进的 T-S 模糊随机时延系统稳定性判据

尹宗明,   仇  磊,   张  宁,   张卫华   

  1. 贵州工程应用技术学院机械工程学院，毕节 551700
  • 收稿日期:2024-05-15 接受日期:2025-01-04 出版日期:2025-08-15 发布日期:2025-10-15
  • 基金资助:
    国家自然科学基金 (52465059)；贵州省基础研究 (自然科学) 项目 (黔科合基础-ZK[2024]一般602号)；贵州省高等学校自然科学研究项目 (黔教技(2024)257号；黔教技(2022)401号)；贵州省高层次创新型人才项目 (毕科人才合(2025)8号)；
    毕节市科学技术项目(毕科联合(2023)18号；毕科联合(2023)43号).

An Improve Stability Criterion for T-S Fuzzy Systems with Random Time-varying Delay

YIN Zongming,   CHOU Lei,   ZHANG Ning,  ZHANG Weihua   

  1. School of Mechanical Engineering, Guizhou University of Engineering Science, Bijie 551700
  • Received:2024-05-15 Accepted:2025-01-04 Online:2025-08-15 Published:2025-10-15
  • Supported by:
    The National Natural Science Foundation of China (52465059); the Guizhou Provincial Basic Research Program (Natural Science) (QianKeHeJiChu-ZK[2024]YiBan602); the Natural Science Research Project of Guizhou Higher Education Institutions of China (QianJiaoJi(2024)257th; QianJiaoJi(2022)401th); the Guizhou Province High Level Innovative Talent Project (BiKeRenCaiHe(2025)8th); the Science and Technology Project of Bijie City (BiKeLianHe(2023)18th; BiKeLianHe(2023)43th). 

摘要：

考虑 T-S 模糊随机时延系统稳定性问题。首先，考虑系统时延的随机时变特性，通过等价变换建立随机变量依赖的等价新系统模型。基于建立的新系统模型，构造能利用系统隶属度函数、随机时延和其导数信息的李雅普诺夫泛函，采用模糊互逆凸积分不等式估计李雅普诺夫泛函求导后出现的二次型积分项，进而，提出新的隶属度函数和时延函数导数依赖的系统稳定性判据。该判据适用于系统随机时延函数变化率已知和未知两种情形，且都能容许较大的时延上界，即具有较小的保守性。最后，通过两个通用数例验证所提稳定性判据的有效性。

关键词: T-S模糊系统, 隶属度函数, 随机时延, 稳定性判据

Abstract:

The stability problem of T-S fuzzy systems with random time-varying delay is investigated in this article. First, a new random variable dependent system model is established by considering the stochastic time-varying characteristics of time-varying delay, and the original systems can be implied by it. Based on the new system model, a suitable Lyapunov functional is constructed that can utilize the information of membership function, random time-varying delay and its derivative. The fuzzy reciprocally convex integral inequality is used to estimate the quadratic integral term from the derivative of the Lyapunov functional, and a new membership function and derivative of delay function dependent system stability criterion is proposed. For both known and unknown cases of system random time-varying delay function, the obtained stability criterion is applicable, and has less conservatism. Finally, the effectiveness of the proposed stability criterion is verified through two numerical examples.

Key words: T-S fuzzy systems, membership function, random time-varying delay, stability criterion

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