数学
李雅普诺夫函数
李雅普诺夫指数
李雅普诺夫方程
分数阶微积分
Lyapunov重新设计
模糊逻辑
控制理论(社会学)
理论(学习稳定性)
应用数学
模糊控制系统
数学优化
计算机科学
非线性系统
人工智能
物理
混乱的
控制(管理)
机器学习
量子力学
作者
Xiaofei Fan,Zhanshan Wang
出处
期刊:IEEE Transactions on Fuzzy Systems
[Institute of Electrical and Electronics Engineers]
日期:2022-07-01
卷期号:30 (7): 2769-2776
被引量:19
标识
DOI:10.1109/tfuzz.2021.3078289
摘要
This article investigates the stability analysis and stabilization problems for fractional-order T–S fuzzy systems via fuzzy Lyapunov function method. A membership-function-dependent fuzzy Lyapunov function instead of the general quadratic Lyapunov function is employed to obtain the stability and stabilization criteria. Different from the general quadratic Lyapunov function, the fuzzy Lyapunov functions contain the product of three term functions. Since the general Leibniz formula cannot be satisfied for fractional derivative, the current results on the fractional derivative for the quadratic Lyapunov functions cannot be extended to the fuzzy Lyapunov functions. Therefore, to estimate the fractional derivative of fuzzy Lyapunov functions, the fractional derivative rule for the product of three term functions is proposed. Based on the proposed fractional derivative rule, the corresponding stability and stabilization criteria are established, which extend the existing results. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical analysis.
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