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

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

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.

Keywords: Hopfield neural networks linear matrix inequality Takagi-Sugeno fuzzy model homogeneous polynomially technique

Received: 10 February 2012
Revised: 28 June 2012
Accepted manuscript online:

PACS:

07.05.Mh

(Neural networks, fuzzy logic, artificial intelligence)

Fund: 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).

Corresponding Authors: Feng Yi-Fu
E-mail: yf19692004@163.com

Cite this article:

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 2012 Chin. Phys. B 21 100701

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

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