Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

• Published in: Chinese physics B Vol. 21; no. 10; pp. 179 - 188
• Main Author: 冯毅夫 张庆灵 冯德志
• Format: Journal Article
• Language: English
• Published: 01.10.2012
• Subjects: Asymptotic properties; Criteria; Functions (mathematics); Fuzzy logic; Lyapunov-Krasovskii泛函; Mathematical analysis; Neural networks; Polynomials; Stability; 基础; 技术; 模糊Hopfield神经网络; 矩阵多项式; 稳定性判据; 线性矩阵不等式; 齐次
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/21/10/100701

The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.