Further improvement of the Lyapunov functional and the delay-dependent stability criterion for a neural network with a constant delay

doi:10.1088/1674-1056/21/4/040701

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.

Keywords: neural system globally asymptotical stability time delay

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)

[1]	Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[2]	Effect of autaptic delay signal on spike-timing precision of single neuron Xuan Ma(马璇), Yaya Zhao(赵鸭鸭), Yafeng Wang(王亚峰), Yueling Chen(陈月玲), and Hengtong Wang(王恒通). Chin. Phys. B, 2023, 32(3): 038703.
[3]	Inferring interactions of time-delayed dynamic networks by random state variable resetting Changbao Deng(邓长宝), Weinuo Jiang(蒋未诺), and Shihong Wang(王世红). Chin. Phys. B, 2022, 31(3): 030502.
[4]	Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Chin. Phys. B, 2022, 31(3): 033101.
[5]	Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[6]	Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Chin. Phys. B, 2022, 31(10): 100201.
[7]	Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns Ben Cao(曹奔), Huaguang Gu(古华光), and Yuye Li(李玉叶). Chin. Phys. B, 2021, 30(5): 050502.
[8]	Stabilization strategy of a car-following model with multiple time delays of the drivers Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2021, 30(12): 120506.
[9]	Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay Guoyuan Qi(齐国元) and Zimou Wang(王子谋). Chin. Phys. B, 2021, 30(12): 120516.
[10]	Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks Yu-Jiao Huang(黄玉娇), Xiao-Yan Yuan(袁孝焰), Xu-Hua Yang(杨旭华), Hai-Xia Long(龙海霞), Jie Xiao(肖杰). Chin. Phys. B, 2020, 29(2): 020703.
[11]	Enhanced vibrational resonance in a single neuron with chemical autapse for signal detection Zhiwei He(何志威), Chenggui Yao(姚成贵), Jianwei Shuai(帅建伟), and Tadashi Nakano. Chin. Phys. B, 2020, 29(12): 128702.
[12]	Design of passive filters for time-delay neural networks with quantized output Jing Han(韩静), Zhi Zhang(章枝), Xuefeng Zhang(张学锋), and Jianping Zhou(周建平). Chin. Phys. B, 2020, 29(11): 110201.
[13]	Validity of extracting photoionization time delay from the first moment of streaking spectrogram Chang-Li Wei(魏长立), Xi Zhao(赵曦). Chin. Phys. B, 2019, 28(1): 013201.
[14]	Synchronization performance in time-delayed random networks induced by diversity in system parameter Yu Qian(钱郁), Hongyan Gao(高红艳), Chenggui Yao(姚成贵), Xiaohua Cui(崔晓华), Jun Ma(马军). Chin. Phys. B, 2018, 27(10): 108902.
[15]	Attosecond transient absorption spectroscopy: Comparative study based on three-level modeling Zeng-Qiang Yang(杨增强), Di-Fa Ye(叶地发), Li-Bin Fu(傅立斌). Chin. Phys. B, 2018, 27(1): 013301.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Further improvement of the Lyapunov functional and the delay-dependent stability criterion for a neural network with a constant delay

Cite this article:

Online attention