Skip to main content

Synchronization of Complex Networks with Time-Varying Coupling Delay via Impulsive Control

  • Conference paper

Abstract

Impulsive control and exponential synchronization analysis of a class of complex networks with time-varying coupling delay is investigated in this paper. Our aim is to enhance the synchronizability of the complex networks by applying impulsive control. By introducing a comparison system and estimating the corresponding Cauchy matrix sufficient conditions on global exponential synchronization are derived. An impulsive controller is explicitly designed not only to achieve synchronized dynamics for the complex networks, but simultaneously to ensure the states of synchronous error converging with a given decay rate. A numerical example is presented to illustrate the theoretical results and proposed controller design procedure.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Watts, D.J.: Small-worlds: The dynamics of networks between order and randomness. Princeton University Press, Princeton (1999)

    MATH  Google Scholar 

  2. Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)

    Article  Google Scholar 

  3. Wang, X., Chen, G.: Complex networks: small-world, scale-free and beyond. IEEE Circuits Syst. Mag. 3, 6–20 (2003)

    Article  Google Scholar 

  4. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: Structure and dynamics. Physics Reports 424, 175–308 (2006)

    Article  MathSciNet  Google Scholar 

  5. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  6. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1991)

    MathSciNet  MATH  Google Scholar 

  7. Wu, C.: Synchronization in coupled chaotic circuits and systems. World Scientific, Singapore (2002)

    Book  MATH  Google Scholar 

  8. Wu, C.: Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuit Syst. II 52, 282–286 (2005)

    Article  Google Scholar 

  9. Zhou, C., Kurths, J.: Dynamical weights and enhanced synchronization in adaptive complex networks. Phys. Rev. Lett. 96, 164102 (2006)

    Article  Google Scholar 

  10. Li, Z., Chen, G.: Global synchronization and asymptotic stability of complex dynamical networks. IEEE Trans. Circuit Syst. II 53, 28–33 (2006)

    Article  Google Scholar 

  11. Lü, J., Yu, X., Chen, G., Cheng, D.: Characterizing the synchronizability of small-world dynamical networks. IEEE Trans. Circuit Syst. I 51, 787–796 (2004)

    Article  MathSciNet  Google Scholar 

  12. Wang, X., Chen, G.: Synchronization in scale-free dynamical networks: Robustness and fragility. IEEE Trans. Circuit Syst. I 49, 54–62 (2002)

    Article  MathSciNet  Google Scholar 

  13. Zhou, J., Chen, T.: Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuit Syst. I 53, 733–744 (2006)

    Article  MathSciNet  Google Scholar 

  14. Dai, Y., Cai, Y., Xu, X.: Synchronization criteria for complex dynamical networks with neutral-type coupling delay. Physica A 387, 4673–4682 (2008)

    Article  Google Scholar 

  15. Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circuit Syst. I 51, 2074–2087 (2004)

    Article  MathSciNet  Google Scholar 

  16. Zhou, J., Lu, J., Lü, J.: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Autom. Control 51, 652–656 (2006)

    Article  MathSciNet  Google Scholar 

  17. Wu, J., Jiao, L.: Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers. Physica A 8-9, 2111–2119 (2008)

    Article  MathSciNet  Google Scholar 

  18. Li, P., Cao, J.: Stabilisation and synchronisation of chaotic systems via hybrid control. IET Control Theory Appl. 1, 795–801 (2007)

    Article  Google Scholar 

  19. Yang, T.: Impulsive control theory. Springer, Berlin (2001)

    MATH  Google Scholar 

  20. Liu, B., Liu, X., Chen, G., Wang, H.: Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuit Syst. I 52, 1431–1441 (2005)

    Article  MathSciNet  Google Scholar 

  21. Zhang, G., Liu, Z., Ma, Z.: Synchronization of complex dynamical networks via impulsive control. Chaos 17, 043126 (2007)

    Article  MathSciNet  Google Scholar 

  22. Li, K., Lai, C.: Adaptive impulsive synchronization of uncertain complex dynamical networks. Physics Letters A 372, 1601–1606 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Niculescu, S.I., Gu, K.: Advances in time-delay systems. Springer, Berlin (2004)

    Book  MATH  Google Scholar 

  24. Yang, Z., Xu, D.: Stability analysis and design of impulsive control systems with time delay. IEEE Trans. Autom. Control 52, 1448–1454 (2007)

    Article  MathSciNet  Google Scholar 

  25. Horn, R.A., Johnson, C.R.: Topics in matrix analysis. Cambridge University Press, Cambridge (1991)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

About this paper

Cite this paper

Dai, Y., Cai, Y., Xu, X. (2009). Synchronization of Complex Networks with Time-Varying Coupling Delay via Impulsive Control. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_91

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02466-5_91

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02465-8

  • Online ISBN: 978-3-642-02466-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics