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

doi:10.1088/1674-1056/21/10/100701

中国物理B ›› 2012, Vol. 21 ›› Issue (10): 100701-100701.doi: 10.1088/1674-1056/21/10/100701

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

冯毅夫^a, 张庆灵^b, 冯德志^b

a School of Mathematics, Jilin Normal University, Siping 136000, China;
b Institute of Systems Science, Northeastern University, Shenyang 110004, China

收稿日期:2012-02-10 修回日期:2012-06-28 出版日期:2012-09-01 发布日期:2012-09-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60974004) and the Natural Science Foundation of Jilin Province, China (Grant No. 201115222).

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

Feng Yi-Fu (冯毅夫)^a, Zhang Qing-Ling (张庆灵)^b, Feng De-Zhi (冯德志)^b

a School of Mathematics, Jilin Normal University, Siping 136000, China;
b Institute of Systems Science, Northeastern University, Shenyang 110004, China

Received:2012-02-10 Revised:2012-06-28 Online:2012-09-01 Published:2012-09-01
Contact: Feng Yi-Fu E-mail:yf19692004@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60974004) and the Natural Science Foundation of Jilin Province, China (Grant No. 201115222).

摘要/Abstract

摘要： 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.

关键词: Hopfield neural networks, linear matrix inequality, Takagi-Sugeno fuzzy model, homogeneous polynomially technique

Abstract: 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.

Key words: Hopfield neural networks, linear matrix inequality, Takagi-Sugeno fuzzy model, homogeneous polynomially technique

中图分类号: (Neural networks, fuzzy logic, artificial intelligence)

07.05.Mh

冯毅夫, 张庆灵, 冯德志. Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique[J]. 中国物理B, 2012, 21(10): 100701-100701.

Feng Yi-Fu (冯毅夫), Zhang Qing-Ling (张庆灵), Feng De-Zhi (冯德志). Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique[J]. Chin. Phys. B, 2012, 21(10): 100701-100701.

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

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

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