|
|
Further improvement of the Lyapunov functional and the delay-dependent stability criterion for a neural network with a constant delay |
Qiu Fang(邱芳) a)b)†, Zhang Quan-Xin(张全信)a)b), and Deng Xue-Hui(邓学辉) a) |
a. Department of Mathematics and Information Science, Binzhou University, Binzhou 256603, China;
b. Insititute of Differential Equation and Dynamical System, Binzhou University, Binzhou 256603, China |
|
|
Abstract This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delay-dependent stability condition is derived by using the novel augmented Lyapunov-Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.
|
Received: 12 August 2011
Revised: 23 October 2011
Accepted manuscript online:
|
PACS:
|
07.05.Mh
|
(Neural networks, fuzzy logic, artificial intelligence)
|
|
Fund: Project supported by the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province of China(Grant No.BS2010SF001),Research Fund for the Doctors of Binzhou University(Grant No.2010Y09),and the Natural ScienceFoundation of Shandong Province of China(Grant No.ZR2010AM031) |
Corresponding Authors:
Qiu Fang, E-mail:rgbayqf@yahoo.com.cn
E-mail: rgbayqf@yahoo.com.cn
|
Cite this article:
Qiu Fang(邱芳), Zhang Quan-Xin(张全信), and Deng Xue-Hui(邓学辉) Further improvement of the Lyapunov functional and the delay-dependent stability criterion for a neural network with a constant delay 2012 Chin. Phys. B 21 040701
|
[1] |
Arik S 2004 Neural Netw. 17 1027
|
[2] |
Chen T and Rong L 2003 Phys. Lett. A 317 436
|
[3] |
Rong L 2005 Phys. Lett. A 339 63
|
[4] |
Cao J D and Li X L 2005 Physica D 212 54
|
[5] |
He Y, Wu M and She J H 2006 IEEE Trans. Neural Network 17 250
|
[6] |
Cui B T, Chen J and Lou X Y 2008 Chin. Phys. B 17 1670
|
[7] |
Wu W and Cui B T 2007 Chin. Phys. 16 1889
|
[8] |
Li D, Wang H, Yang D, Zhang X H and Wang S L 2008 Chin. Phys. B 17 4091
|
[9] |
Tan W and Wang Y N 2005 Chin. Phys. 14 72
|
[10] |
Chen D L and Zhang W D 2008 Chin. Phys. B 17 1506
|
[11] |
Xu S Y, Zheng W X and Zou Y 2009 IEEE Trans. Circ. Syst. II 56 325
|
[12] |
Zhang W Y and Li J M 2011 Chin. Phys. B 20 030701
|
[13] |
Yao H X and Zhou J Y 2011 Chin. Phys. B 20 010701
|
[14] |
Liao X F and Li C D2005 Physica D 200 139
|
[15] |
Li C D, Liao X F and Zhang R 2004 Phys. Lett. A 328 452
|
[16] |
Liao T L, Yan J J, Cheng C J and Wang C C 2005 Phys. Lett. A 339 333
|
[17] |
Luo Q, Deng F Q and Bao J D 2006 Acta Phys. Sin. 55 968 (in Chinese)
|
[18] |
Zeng Z G and Liao X X 2005 Acta Phys. Sin. 54 621 (in Chinese)
|
[19] |
Zhang Y and Zhang Z Y 2011 Acta Phys. Sin. 60 090703 (in Chinese)
|
[20] |
Lu J G 2007 IEEE Trans. Circ. Syst. II 54 1115
|
[21] |
Lu J G 2008 Chaos, Solitons and Fractals 35 116
|
[22] |
Lakshmanan S and Balasubramaniam P 2011 Chin. Phys. B 20 040204
|
[23] |
Xu S Y, Lam J, Ho D W C and Zhou Y 2005 IEEE Trans. Circ. Syst. II 52 349
|
[24] |
Hua C C, Long C N and Guan X P 2006 Phys. Lett. A 352 335
|
[25] |
Fridman E and Shaked U 2003 IEEE Trans. Automat. Control 48 861
|
[26] |
He Y, Liu G P and Rees D 2007 IEEE Trans. Neural Netw. 18 310
|
[27] |
Parlakci M N A 2008 IET Control Theory Appl. 2 431
|
[28] |
Shao H Y 2008 IEEE Trans. Circ. Syst. II 55 1071
|
[29] |
He Y, Wang Qi G, Lin C and Wu M 2005 Int. J. Robust Nonlinear Control 15 923
|
[30] |
Kwon O M, Park J H and Lee S M 2009 Appl. Math. Comput. 207 202
|
[31] |
Rakkiyappan R, Balasubramaniam P and Krishnasamy R 2011 J. Comput. Appl. Math. 235 2147
|
[32] |
Qiu F and Cui B T 2009 Chin. Phys. B 18 473
|
[33] |
Sun J, Liu G P and Chen J 2009 Int. J. Robust Nonlinear Control 19 1364
|
[34] |
Hale J K and Verduyn Lunel S M 1993 Introduction to Functional Differential Equations (Applied Mathematical Sciences) (New York: Springer-Verlag)
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|