H∞ synchronization of chaotic neural networks with time-varying delays

doi:10.1088/1674-1056/22/11/110504

Abstract In this paper, we investigate the problem of H_∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By constructing a suitable Lyapunov–Krasovskii functional and using a reciprocally convex approach, a novel H_∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Keywords: chaotic neural networks time-varying delays H_∞ synchronization Lyapunov method

Received: 01 March 2013
Revised: 06 May 2013
Accepted manuscript online:

PACS:	05.65.+b	(Self-organized systems)
	02.01.Yn

Fund: Project supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. 2012-0000479) and the Korea Healthcare Technology R&D Project, Ministry of Health and Welfare, Republic of Korea (Grant No. A100054).

Corresponding Authors: Ju H. Park
E-mail: jessie@ynu.ac.kr

Cite this article:

O. M. Kwon, M. J. Park, Ju H. Park, S. M. Lee, E. J. Cha H_∞ synchronization of chaotic neural networks with time-varying delays 2013 Chin. Phys. B 22 110504

[1]	Pecora L M and Carroll T L 1990 Phys. Lett. 64 821
[2]	Pecora L M and Carroll T L 1991 IEEE Trans. Circ. Syst. 38 453
[3]	Kwon O M, Park Ju H and Lee S M 2011 Nonlinear Dyn. 63 239
[4]	Lee S M, Kwon O M and Park Ju H 2011 Chin. Phys. B 20 010506
[5]	Sun F Y 2006 Chin. Phys. Lett. 23 32
[6]	Wang J G and Zhao Y 2005 Chin. Phys. Lett. 22 2508
[7]	Wu Z Q and Kuang Y 2009 Acta Phys. Sin. 58 6823 (in Chinese)
[8]	Guan X P and Hua C C 2002 Chin. Phys. Lett. 19 1031
[9]	Feki M 2003 Chaos Soliton. Fract. 18 141
[10]	Gilli M 1993 IEEE Trans. Circ. Syst. 40 849
[11]	Lu H T 2002 Phys. Lett. A 298 109
[12]	Lee T H, Park J H, Lee S M and Kwon O M 2013 Int. J. Control 86 107
[13]	Kwon O M and Park J H 2008 Appl. Math. Comput. 205 417
[14]	Balasubramaniam P and Lakshmanan S 2009 Nonlinear Anal.: Hybrid Syst. 3 749
[15]	Kwon O M, Kwon J W and Kim S H 2011 Chin. Phys. B 20 050505
[16]	Wu Z G, Shi P, Su H and Chu J 2012 IEEE Trans. Neural Netw. Learn. Syst. 23 199
[17]	Mathiyalagan K, Sakthivel R and Anthoni S M 2012 Phys. Lett. A 376 901
[18]	Li T, Zheng W X and Lin C 2011 IEEE Trans. Neural Netw. 22 2138
[19]	Kwon O M and Park J H 2009 Phys. Lett. A 373 529
[20]	Li T, Fei S M, Zhu Q and Cong S 2008 Neurocomputing 71 3005
[21]	Li T, Song A G, Fei S M and Guo Y Q 2009 Nonlinear Anal.-Theory Methods Appl. 71 2372
[22]	Cui B and Lou X 2009 Chaos Soliton. Fract. 39 288
[23]	Hu J 2009 Chaos Soliton. Fract. 41 2495
[24]	Balasubramaniam P, Chandran R and Jeeva Sathya Theesar S 2011 Cogn. Neurodyn. 5 361
[25]	Zames G 1981 IEEE Trans. Autom. Control 26 301
[26]	Gao H, Wu J and Shi P 2009 Automatica 45 1729
[27]	Yan H, Zhang H and Meng M Q H 2010 Neurocomputing 73 1235
[28]	Tan K and Grigoriadis K M 2001 Syst. Contr. Lett. 44 57
[29]	Park Ju H, Ji D H, Won S C and Lee S M 2008 Appl. Math. Comput. 204 170
[30]	Lee S M, Ji D H, Park Ju H and Won S C 2008 Phys. Lett. A 372 4905
[31]	Karimi H R and Gao H 2010 IEEE Trans. Syst. Man Cybern. Part B-Cybern. 40 173
[32]	Qi D, Qiu M and Zhang S 2010 IEEE Trans. Neural Netw. 21 1358
[33]	Karimi H R 2012 J. Franklin Inst. 349 1480
[34]	Wang B, Shi P, Karimi H R, Song Y and Wang J 2013 Nonl. Anal. Real World Appl. 14 1487
[35]	Li H 2013 Appl. Math. Model. 37 7223
[36]	Kim S H, Park P and Jeong C 2010 IET Contr. Theory Appl. 4 1828
[37]	Park P G, Ko J W and Jeong C 2011 Automatica 47 235
[38]	Clarke F H 1983 Optimization and Nonsmooth Analysis (New York: Wiley)
[39]	Anton S 1992 The H∞ Control Problem (New York: Prentice Hall)
[40]	Boyd S, El Ghaoui L, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM)
[41]	Gu K 2000 Proc. IEEE Conf. Decision Control, December 12–15, 2000, Sydney, Australia, pp. 2805–2810.

[1]	Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay Mei Li(李梅), Ruo-Xun Zhang(张若洵), and Shi-Ping Yang(杨世平). Chin. Phys. B, 2021, 30(12): 120503.
[2]	Application of the edge of chaos in combinatorial optimization Yanqing Tang(唐彦卿), Nayue Zhang(张娜月), Ping Zhu(朱萍), Minghu Fang(方明虎), and Guoguang He(何国光). Chin. Phys. B, 2021, 30(10): 100505.
[3]	Robust H_∞ control for uncertain Markovian jump systems with mixed delays R Saravanakumar, M Syed Ali. Chin. Phys. B, 2016, 25(7): 070201.
[4]	Robust H_∞ control of uncertain systems with two additive time-varying delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2015, 24(9): 090202.
[5]	Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays M. Syed Ali. Chin. Phys. B, 2014, 23(6): 060702.
[6]	Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays R. Rakkiyappan, N. Sakthivel, S. Lakshmanan. Chin. Phys. B, 2014, 23(2): 020205.
[7]	Leader–following consensus control for networked multi-teleoperator systems with interval time-varying communication delays M. J. Park, S. M. Lee, J. W. Son, O. M. Kwon, E. J. Cha. Chin. Phys. B, 2013, 22(7): 070506.
[8]	Adaptive H_∞ synchronization of chaotic systems via linear and nonlinear feedback control Fu Shi-Hui(付士慧), Lu Qi-Shao(陆启韶), and Du Ying(杜莹) . Chin. Phys. B, 2012, 21(6): 060507.
[9]	Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes Wang Shu-Guo(王树国) and Yao Hong-Xing(姚洪兴) . Chin. Phys. B, 2012, 21(5): 050508.
[10]	Leader–following consensus criteria for multi-agent systems with time-varying delays and switching interconnection topologies M. J. Park, O. M. Kwon, Ju H. Park, S. M. Lee, E. J. Cha. Chin. Phys. B, 2012, 21(11): 110508.
[11]	Robust stability analysis of Takagi–Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays M. Syed Ali . Chin. Phys. B, 2011, 20(8): 080201.
[12]	New results on stability criteria for neural networks with time-varying delays O.M. Kwon, J.W. Kwon, and S.H. Kim. Chin. Phys. B, 2011, 20(5): 050505.
[13]	Synchronization criteria for coupled Hopfield neural networks with time-varying delays M.J. Park, O.M. Kwon, Ju H. Park, S.M. Lee, and E.J. Cha . Chin. Phys. B, 2011, 20(11): 110504.
[14]	Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network Jin Xiao-Zheng(金小峥) and Yang Guang-Hong (杨光红). Chin. Phys. B, 2010, 19(8): 080508.
[15]	Improved delay-dependent globally asymptotic stability of delayed uncertain recurrent neural networks with Markovian jumping parameters Ji Yan(籍艳) and Cui Bao-Tong(崔宝同). Chin. Phys. B, 2010, 19(6): 060512.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

H∞ synchronization of chaotic neural networks with time-varying delays

Cite this article:

Online attention

H_∞ synchronization of chaotic neural networks with time-varying delays