Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays

doi:10.1088/1674-1056/23/6/060702

Abstract In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen-Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples.

Keywords: Cohen-Grossberg neural networks global asymptotic stability linear matrix inequality Lyapunov functional time-varying delays

Received: 12 November 2013
Revised: 12 December 2013
Accepted manuscript online:

PACS:	07.05.Mh	(Neural networks, fuzzy logic, artificial intelligence)
	05.45.Gg	(Control of chaos, applications of chaos)
	02.30.Ks	(Delay and functional equations)
	02.30.Sa	(Functional analysis)

Fund: Project supported by DST Project (Grant No. SR/FTP/MS-039/2011).

Corresponding Authors: M. Syed Ali
E-mail: syedgru@gmail.com

Cite this article:

M. Syed Ali Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays 2014 Chin. Phys. B 23 060702

[1]	Cohen M A and Grossberg S 1983 IEEE Trans. Syst., Man, Cybern. 13 815
[2]	Ji C, Zhang H G and Wang Z S 2004 Control Decision 19 1416
[3]	Yuan K, Cao J and Li H X 2006 IEEE Trans. Syst. Man Cybern. Part B Cybern. 36 1356
[4]	Takahashi Y 1996 Theor. Comput. Sci. 158 279
[5]	Wang L and Zou X 2002 Physica D 170 162
[6]	Bai C 2008 Nonlinear Anal.: Real World Appl. 9 747
[7]	Xia Y, Huang Z and Han M 2008 Chaos, Solitons and Fractals 38 806
[8]	Zhao W 2008 Commun. Nonlinear Sci. Numer. Simul. 13 847
[9]	Huang H and Cao J 2007 Nonlinear Anal: Real World Appl. 8 646
[10]	Wang Z, Lauria S, Fang J and Liu X 2007 Chaos, Solitons and Fractals 32 62
[11]	Zhu Q X and Cao J D 2010 IEEE Trans. Neural Networks 21 1314
[12]	Liu Y R, Wang Z D and Liu X 2006 Neural Networks 19 667
[13]	Balasubramaniam P, Lakshmanan S and Rakkiyappan R 2009 Neurocomput. 72 3675
[14]	Kwon O M, Lee S M, Park Ju H and Cha E J 2012 Appl. Math. Comput. 218 9953
[15]	Li X 2010 Appl. Math. Comput. 215 4370
[16]	Cui B T, Chen J and Lou X Y 2008 Chin. Phys. B 17 1670
[17]	Wu W and Cui B T 2007 Chin. Phys. 16 1889
[18]	Li D, Wang H, Yang D, Zhang X H and Wang S L 2008 Chin. Phys. B 17 4091
[19]	Tan W and Wang Y N 2005 Chin. Phys. 14 72
[20]	Chen D L and Zhang W D 2008 Chin. Phys. B 17 1506
[21]	Zhang W Y and Li J M 2011 Chin. Phys. B 20 030701
[22]	Yao H X and Zhou J Y 2011 Chin. Phys. B 20 010701
[23]	Lien C H and Chung L Y 2007 Chaos, Solitons and Fractals 34 1213
[24]	Mahmoud M S and Xia Y 2011 J. Franklin Inst. 348 201
[25]	Lee T H, Park J H, Kwon O M and Lee S M 2013 Neural Netw. 46 99
[26]	Wu Z G, Park J H, Su H and Chu J 2013 Commun. Nonlinear Sci. Numer. Simul. 18 669
[27]	Wu Z G, Park J H, Su H and Chu J 2012 Nonlinear Dynamics 70 825
[28]	Wu Z G, Park J H, Su H and Chu J 2012 Nonlinear Dynamics 69 2021
[29]	Wu Z G, Park J H, Su H and Chu J 2012 Nonlinear Anal. RWA 13 1593
[30]	Orman Z 2012 Neurocomput. 97 141
[31]	Park J H and Kwon O M 2009 Mod. Phys. Lett. B 23 35
[32]	Samli R and Arik S 2009 Appl. Math. Comput. 210 564
[33]	Shen Y and Wang J 2007 IEEE Trans. Neural Netw. 18 1857
[34]	Shen Y and Wang J 2009 IEEE Trans. Neural Netw. 20 840
[35]	Zhang G, Shen Y, Yin Q and Sung J 2013 Information Sciences 232 386
[36]	Syed Ali M and Balasubramaniam P 2009 Commun. Nonlinear Sci. Numer. Simul. 14 2776
[37]	Syed Ali M and Balasubramaniam P 2009 Neurocomput. 72 1347
[38]	Gan Q and Xu R 2010 Neural Process. Lett. 32 83
[39]	Ma Q, Xu S, Zou Y and Lu J 2011 Neurocomput. 74 2157
[40]	Tian J, Li Y, Zhao J and Zhong S 2012 Appl. Math. Comput. 218 5769
[41]	Yu J and Sun G 2012 Neurocomput. 86 107
[42]	Zhang H, Dong M, Wang Y C and Sun N 2010 Neurocomput. 73 2689
[43]	Zhu S, Shen Y and Liu L 2010 Neural Process Lett. 32 293
[44]	Zhu Q X and Cao J D 2011 IEEE Trans. Syst. Man Cybern. B 41 341
[45]	Gahinet P, Nemirovski A, Laub A and Chilali M 1995 LMI Control Toolbox User's Guide (Massachusetts: The Mathworks)
[46]	Boyd B, Ghoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadephia: SIAM)
[47]	Mao X and Yuan C 2006 Stochastic Differential Equations with Markovian Switching (London: Imperial College Press)
[48]	Khasminski R 1980 Stochastic Stability of Differential Equations (Netherlands: Sijithoff and Noordhoff)
[49]	Gu K, Kharitonov V L and Chen J 2003 Stability of Time Delay Systems (Boston: Birkhuser)
[50]	Wang Y, Xie L and de Souza C E 1992 Systems Control Lett. 19 139
[51]	Chen W H, Guan Z H and Lu X M 2004 IMA I Math. Control Informat. 21 345
[52]	Wang Z, Liu Y, Li M and Liu X 2006 IEEE Trans. Neural Netw. 17 814
[53]	Rong L 2005 Phys. Lett. A 339 63
[54]	Zhang H and Wang Y 2008 IEEE Trans. Neural Netw. 19 366

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Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays

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