Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays

doi:10.1088/1674-1056/20/3/030701

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30701-030701.doi: 10.1088/1674-1056/20/3/030701

Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays

李俊民¹, 张为元²

(1)School of Science, Xidian University, Xi'an 710071, China; (2)School of Science, Xidian University, Xi'an 710071, China;Institute of Math. and Applied Math., Xianyang Normal University, Xianyang 712000, China

收稿日期:2010-07-07 修回日期:2010-09-28 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project partially supported by the National Natural Science Foundation of China (Grant No. 60974139) and partially supported by the Fundamental Research Funds for the Central Universities.

Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays

Zhang Wei-Yuan(张为元)^a)b)† and Li Jun-Min(李俊民)^a)‡

^a School of Science, Xidian University, Xi'an 710071, China; ^b Institute of Math. and Applied Math., Xianyang Normal University, Xianyang 712000, China

Received:2010-07-07 Revised:2010-09-28 Online:2011-03-15 Published:2011-03-15
Supported by:
Project partially supported by the National Natural Science Foundation of China (Grant No. 60974139) and partially supported by the Fundamental Research Funds for the Central Universities.

摘要/Abstract

摘要： This paper investigates the global exponential stability of reaction--diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov--Krasovskii functional combined with a free-weighting matrix approach and analysis techniques, delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities. The obtained results are dependent on the size of the time-varying delays and the measure of the space, which are usually less conservative than delay-independent and space-independent ones. These results are easy to check, and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. A numerical example has been presented to show the usefulness of the derived linear matrix inequality (LMI)-based stability conditions.

关键词: neural networks, reaction–diffusion, delays, exponential stability

Abstract: This paper investigates the global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov–Krasovskii functional combined with a free-weighting matrix approach and analysis techniques, delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities. The obtained results are dependent on the size of the time-varying delays and the measure of the space, which are usually less conservative than delay-independent and space-independent ones. These results are easy to check, and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. A numerical example has been presented to show the usefulness of the derived linear matrix inequality (LMI)-based stability conditions.

Key words: neural networks, reaction–diffusion, delays, exponential stability

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

07.05.Mh

张为元, 李俊民. Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays[J]. 中国物理B, 2011, 20(3): 30701-030701.

Zhang Wei-Yuan(张为元) and Li Jun-Min(李俊民). Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays[J]. Chin. Phys. B, 2011, 20(3): 30701-030701.

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Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays

Global exponential stability of reaction–diffusion neural networks with discrete and distributed time-varying delays

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