Global synchronization of general delayed complex networks with stochastic disturbances

doi:10.1088/1674-1056/20/3/030504

Abstract In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, ItÔ's differential rule and the linear matrix inequality (LMI) optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.

Keywords: global synchronization general delayed complex networks with stochastic disturbances linear matrix inequality mean-square stability

Received: 16 May 2010
Revised: 26 September 2010
Accepted manuscript online:

PACS:	05.40.Ca	(Noise)
	05.45.Xc

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60904060), and the Open Foundation of Hubei Province Key Laboratory of Systems Science in Metallurgical Process, China (Grant No. C201010).

Cite this article:

Tu Li-Lan(涂俐兰) Global synchronization of general delayed complex networks with stochastic disturbances 2011 Chin. Phys. B 20 030504

[1]	Strogatz S H 2001 Nature 410 268
[2]	Albert R and Barab'asi A L 2002 Rev. Mod. Phys. 74 47
[3]	Tomassini M, Pestelacci E and Luthi L 2007 Int. J. Modern Phys. C 18 1173
[4]	Gao Y, Li L X, Peng H P, Yang Y X and Zhang X H 2008 Acta Phys. Sin. 57 1444 (in Chinese)
[5]	Wang H X, Lu Q S and Shi X 2010 Chin. Phys. B 19 060509
[6]	Zou Y L and Chen G R 2009 Chin. Phys. B 18 3337
[7]	Ma X J, Wang Y and Zheng Z G 2009 Acta Phys. Sin. 58 4426 (in Chinese)
[8]	Bennett M V L and Zukin R S 2004 Neuron. 41 495
[9]	Wang X F and Cheng G R 2002 Physica A 310 521
[10]	Li X, Wang X F and Chen G 2004 IEEE Trans. Circuits Syst. I 51 2074
[11]	Chen G, Zhou J and Liu Z 2004 Int. J. Bifurc. Chaos 14 2229
[12]	L"u J H and Chen G R 2005 IEEE Trans. Autom. Control. 50 841
[13]	Zhou J and Chen T 2006 IEEE TCAS 53 733
[14]	Zhan M, Gao J H, Wu Y and Xiao J H 2007 Phys. Rev. E 76 036203
[15]	Xiang L Y, Liu Z X, Chen Z Q and Yuan Z Z 2008 Sci. China Ser F-Inf Sci. 51 511
[16]	Wang L, Dai H P, Dong H, Cao Y Y and Sun Y X 2008 Eur. Phys. J. B 61 335
[17]	Zhou J, Lu J A and L"u J H 2009 Automatica 45 598
[18]	Tu L L and Lu J A 2009 Computers and Mathematics with Applications 57 28
[19]	Doyle J C, Alderson D L and Li L 2005 PNAS 102 14497
[20]	Aldana M, Ballezaa E, Kauffmanb S and Resendiz O 2007 Journal of Theoretical Biology 245 433
[21]	Zhao L, Park K and Lai Y C 2004 Phys. Rev. E 70 035101
[22]	Liang J L, Wang Z D and Liu X H 2008 Nonlinear Dyn. 53 153
[23]	Liang J L, Wang Z D Liu Y R and Liu X H 2008 IEEE Trans. Syst. Man Cybern. B 38 1073
[24]	Park J H, Lee S M and Jung H Y 2009 J. Optim. Theory Appl. 143 357
[25]	Sun Y, Cao J and Wang Z 2007 Neurocomputing 70 2477
[26]	Wang Y, Wang Z D and Liang J L 2008 Phys. Lett. A 372 6066
[27]	Li H J and Yue D 2010 J. Phys. A: Math. Theor. 43 105101
[28]	Li Z K, Duan Z S and Chen G R 2009 Chin. Phys. B 18 5228
[29]	Boyd S, Ghaoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM) 7 endfootnotesize

[1]	Adaptive synchronization of chaotic systems with less measurement and actuation Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚). Chin. Phys. B, 2021, 30(10): 100503.
[2]	Robust H_∞ control for uncertain Markovian jump systems with mixed delays R Saravanakumar, M Syed Ali. Chin. Phys. B, 2016, 25(7): 070201.
[3]	Robust H_∞ control of uncertain systems with two additive time-varying delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2015, 24(9): 090202.
[4]	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.
[5]	Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2014, 23(12): 120201.
[6]	Cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay Wang Jun-Yi (王军义), Zhang Hua-Guang (张化光), Wang Zhan-Shan (王占山), Liang Hong-Jing (梁洪晶). Chin. Phys. B, 2013, 22(9): 090504.
[7]	Novel delay dependent stability analysis of Takagi–Sugeno fuzzy uncertain neural networks with time varying delays M. Syed Ali . Chin. Phys. B, 2012, 21(7): 070207.
[8]	Novel delay-distribution-dependent stability analysis for continuous-time recurrent neural networks with stochastic delay Wang Shen-Quan (王申全), Feng Jian (冯健), Zhao Qing (赵青). Chin. Phys. B, 2012, 21(12): 120701.
[9]	Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback Wang Jun-Wei (王军威), Zeng Cai-Bin (曾才斌 ). Chin. Phys. B, 2012, 21(11): 110206.
[10]	Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique Feng Yi-Fu (冯毅夫), Zhang Qing-Ling (张庆灵), Feng De-Zhi (冯德志). Chin. Phys. B, 2012, 21(10): 100701.
[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]	A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control Wang Jun-Wei(王军威), Ma Qing-Hua(马庆华), and Zeng Li(曾丽) . Chin. Phys. B, 2011, 20(8): 080506.
[13]	The $\mathscr{H}_{\infty}$ synchronization of nonlinear Bloch systems via dynamic feedback control approach D.H. Ji, J.H. Koo, S.C. Won, and Ju H. Park. Chin. Phys. B, 2011, 20(7): 070502.
[14]	Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay S. Lakshmanan and P. Balasubramaniam. Chin. Phys. B, 2011, 20(4): 040204.
[15]	New synchronization analysis for complex networks with variable delays Zhang Hua-Guang(张化光), Gong Da-Wei(宫大为), and Wang Zhan-Shan(王占山) . Chin. Phys. B, 2011, 20(4): 040512.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Global synchronization of general delayed complex networks with stochastic disturbances

Cite this article:

Online attention