Wuhan University Journal of Natural Sciences

, Volume 18, Issue 6, pp 471–476 | Cite as

Delay-dependent H synchronization for general delayed complex networks with stochastic disturbances

Article

Abstract

In this paper, the H synchronization is intensively investigated for general delayed complex dynamical networks. The network under consideration contains unknown but bounded nonlinear coupling functions, time-varying delay, external disturbances, and Itô-type stochastic disturbances, which is a zero-mean real scalar Wiener process. Based on the stochastic Lyapunov stability theory, Itô’s differential rule, and linear matrix inequality (LMI) optimization technique, some delay-dependent H synchronization schemes are established, which guarantee robust stochastically mean square asymptotically synchronization for drive network and noise-perturbed response network as well as achieving a prescribed stochastic robust H performance level. Finally, detailed and satisfactory numerical results have validated the feasibility and the correctness of the proposed techniques.

Key words

delay-dependent H synchronization general delayed complex networks with stochastic disturbances linear matrix inequality (LMI) mean-square stability 

CLC number

O 231.5 

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References

  1. [1]
    Wu X, Zheng W, Zhou J. Generalized outer synchronization between complex dynamical networks [J]. Chaos, 2009, 19: 013109.PubMedCrossRefGoogle Scholar
  2. [2]
    Wang H, Song Q. Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays [J]. Neurocomputing, 2011, 74: 1572–1584.CrossRefGoogle Scholar
  3. [3]
    Zhou W, Wang T, Mou J. Synchronization control for the competitive complex networks with time delay and stochastic effects [J]. Commun Nonlinear Sci Numer Simulat, 2012, 17: 3417–3426.CrossRefGoogle Scholar
  4. [4]
    Wu X, Lu H. Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control [J]. Neurocomputing, 2012, 89: 168–177.CrossRefGoogle Scholar
  5. [5]
    Wu X. Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay [J]. Physica A, 2008, 387: 997–1008.CrossRefGoogle Scholar
  6. [6]
    Aldana M, Ballezaa E, Kauffmanb S. Robustness and evolvability in genetic regulatory networks [J]. Journal of Theoretical Biology, 2007, 245: 433–448.PubMedCrossRefGoogle Scholar
  7. [7]
    Zhao L, Park K, Lai Y C. Attack vulnerability of scale-free networks due to cascading breakdown [J]. Physical Review E, 2004, 70: 035101–4.CrossRefGoogle Scholar
  8. [8]
    Liang J L, Wang Z D, Liu X H. Exponential synchronization of stochastic delayed discrete-time complex networks [J]. Nonlinear Dyn, 2008, 53: 153–165.CrossRefGoogle Scholar
  9. [9]
    Li H J, Yue D. Synchronization of Markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time-varying delays [J]. J Phys A: Math Theor, 2010, 43: 105101.CrossRefGoogle Scholar
  10. [10]
    Wang Y, Wang Z D, Liang J L. Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances [J]. Journal of Physics A: Mathematical and Theoretical, 2009, 42: 135101.CrossRefGoogle Scholar
  11. [11]
    Zhang W, Chen B S, Tseng C S. Robust H filtering for nonlinear stochastic systems [J]. IEEE Trans Signal Process, 2005, 53: 589–598.CrossRefGoogle Scholar
  12. [12]
    Xu S Y, Shi P, Chu Y M, Zou Y. Robust stochastic stabilization and H control of uncertain neutral stochastic time-delay systems [J]. J Math Anal Appl, 2006, 314: 1–16.CrossRefGoogle Scholar
  13. [13]
    Wang Z D, Liu Y R, Liu X H. H filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities [J]. Automatica, 2008, 44: 1268–1277.CrossRefGoogle Scholar
  14. [14]
    Boyd S, Ghaoui L E, Feron E, et al. Linear Matrix Inequalities in System and Control Theory [M]. Philadelphia: SIAM, 1994.Google Scholar
  15. [15]
    Anton S. The H Control Problem [M]. New York: Prentice-Hall, 1992.Google Scholar
  16. [16]
    Tu L L, Lu J A. Delay-dependent synchronization in general complex delayed dynamical networks [J]. Computers and Mathematics with Applications, 2009, 57: 28–36.CrossRefGoogle Scholar

Copyright information

© Wuhan University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Hubei Province Key Laboratory of Systems Science in Metallurgical ProcessWuhan University of Science and TechnologyWuhanHubei, China

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