|
|
A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional |
S. M. Leea)†, O. M. Kwonb)‡, and Ju H. Park c)* |
a Department of Electronic Engineering, Daegu University, Gyungsan, Gyungbuk 712-714, Republic of Korea; b College of Electrical and Computer Engineering, 410 SungBong-Ro, Heungduk-Gu, Chungbuk National University, Cheongju 361-763, Republic of Korea; c Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 214-1 Dae-Dong, Kyongsan 712-749, Republic of Korea |
|
|
Abstract In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities (LMIs) by constructing new Lyapunov--Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.
|
Received: 19 August 2009
Revised: 29 October 2009
Accepted manuscript online:
|
PACS:
|
07.05.Mh
|
(Neural networks, fuzzy logic, artificial intelligence)
|
|
02.10.Yn
|
(Matrix theory)
|
|
02.30.Yy
|
(Control theory)
|
|
02.60.Dc
|
(Numerical linear algebra)
|
|
Cite this article:
S. M. Lee, O. M. Kwon, and Ju H. Park A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov--Krasovskii functional 2010 Chin. Phys. B 19 050507
|
[1] |
Tao Q, Cao J, Xue M and Qiao H 2001 Phys. Lett. A 288 88
|
[2] |
Cannas B, Cincotti S, Marchesi M and Pilo F 2001 Chaos, Solitons and Fractals 12 2109
|
[3] |
van Putten M and Stam C J 2001 Phys. Lett. A 281 131
|
[4] |
Gu K, Kharitonov V L and Chen J 2003 Stability of Time-Delay Systems (Boston: Birkhauser)
|
[5] |
Ensari T and Arik S 2005 IEEE Trans. Automat. Contr. 11 1781
|
[6] |
Xu S, Lam J and Ho D W C 2005 Phys. Lett. A 342 322
|
[7] |
Chen D L and Zhang W D 2008 Chin. Phys. B 17 1506
|
[8] |
Park J H 2006 Phys. Lett. B 349 494
|
[9] |
Li D, Wang Y, Yang D, Zhang X and Wang S 2008 Chin. Phys. B 17 4091
|
[10] |
Park J H and Kwon O M 2009 Modern Phys. Lett. B 23 1743
|
[11] |
Li T, Guo L, Sun C and Lin C 2008 IEEE Trans. Neural Netw. 19 726
|
[12] |
Chen Y and Wu Y 2009 Neurocomputing 72 1065
|
[13] |
Tang Y, Zhong H H and Fang J A 2008 Chin. Phys. B 17 4080
|
[14] |
Kwon O M and Park J H 2009 Phys. Lett. A 373 529
|
[15] |
Zhang X M and Han Q L 2009 IEEE Trans. Neural Netw. 20 533
|
[16] |
Wang Y and Zuo Z 2007 Lecture Notes in Computer Science 4432 704--712 (Heidelberg Berlin: Spinger-Verlag)
|
[17] |
Hua C, Long C and Guan X 2006 Phys. Lett. A 352 335
|
[18] |
Khalil H K 1996 Nonlinear Systems 2nd Ed. (New Jersey: Prentice Hall, Englewood Cliffs)
|
[19] |
Haddad W M and Kapila V 1995 IEEE Trans. Automatic Control 40 361
|
[20] |
Park P 2002 IEEE Trans. Automatic Contr. 47 308
|
[21] |
Lee S M, Kwon O M and Park J H 2008 Phys. Lett. A 372 4010
|
[22] |
Skelton R E, Iwasaki T and Grigoradis K M 1997 A Unified Algebraic Approach to Linear Control Design (New York: Taylor and Francis)
|
[23] |
Boyd S, Ghaoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM)
|
[24] |
Cao J 2002 Int. J. Syst. Sci. 31 1313
|
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
|
|
|