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Robust impulsive synchronization of linear discrete dynamical networks

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Abstract

This paper aims to study robust impulsive synchronization problem for uncertain linear discrete dynamical network. For the discrete dynamical networks with unknown but bounded linear coupling, by introducing the concept of uniformly positive definite matrix functions, some robust impulsive controllers are designed, which ensure that the state of a discrete dynamical network globally asymptotically synchronizes with an arbitrarily assigned state of an isolate node of the network. This paper also investigates the synchronization problem where the network coupling functions are uncertain but bounded nonlinear functions. Finally,two examples are simulated to illustrate our results.

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References

  1. L. M. Pccora, T. L. Carroll. Synchronization in chaotic systems [J]. Physical Review Letters, 1990,64(8):821–824.

    Article  Google Scholar 

  2. T. L. Carroll, L. M. Pccora. Synchronization in chaotic circuits [J]. IEEE Trans, on Circuits and Systems, 1991,38(4):453–456.

    Article  Google Scholar 

  3. L. Kocarev, U. Parlitz. General approach for chaotic synchronization with application to communication [J]. Physical Review Letters, 1995, 74 (10):5028–5031.

    Article  Google Scholar 

  4. C. Wu, T. Yang, L. Chua. On adaptive synchronization and control of nonlinear dynamical systems [J]. Int. J. Bifurcation Chaos, 1996,6 (3):455–471.

    Article  MATH  Google Scholar 

  5. G. Grassi, S. Mascolo. Nonlinear observer design to synchronize hyper-chaotic systems via a scalar signal [J]. IEEE Trans, on Circuits and Systems, 1997,44(8): 1011–1014.

    Google Scholar 

  6. L. Kocarev, G. M. Maggio, M. Ogorzalek, et al. Introduction to the special issue [J]. IEEE Trans. on Circuits and Systems, 2001,48(9): 1385–1386.

    MATH  Google Scholar 

  7. G. Chen, X. Dong. On feedback control of chaotic continuous-time systems [J]. IEEE Trans. on Circuits and Systems, 1993,40(3):591–601.

    MATH  Google Scholar 

  8. M. E. Yalcin,J. A. K. Suykens, J. Vandewalle. Master-slave synchronization of Lur’e systems with time-delay [J]. Int. J. Bifurcation Chaos, 2001, 11(11):1707–1772.

    Article  Google Scholar 

  9. T. Yang, L.O. Chua. Impulsive stabilization for control and synchronization of chaotic systems: Theory and application to secure communication[J]. IEEE Trans.on Circuits and Systems, 1997,44(10):976–988.

    Article  Google Scholar 

  10. X. Wang, G. Chen. Synchronization in small-world dynamical networks[J]. Int. J. Bifurcation Chaos, 2002,12(1): 187–192.

    Article  Google Scholar 

  11. X. Wang, G. Chen. Synchronization in scale-free dynamical networks: Robustness and Fragility [J]. IEEE Trans, on Circuits and Systems, 2002,49(l):54–62.

    Google Scholar 

  12. J. Jost,M.P. Joy. Special properties and synchronization in coupled map lattices [J]. Physics Review E., 2002,65(1):6201–6210.

    Google Scholar 

  13. P.M. Grade, C. K. Hu. Synchronization chaos in coupuled map lattices with small-world interactions [J]. Physics Review E., 2000,62(5): 6409–6413.

    Article  Google Scholar 

  14. Z. Li, G. Chen. Robust adaptive synchronization of uncertain dynamical networks [J]. Physics Letter A, 2004,324(2): 166–178.

    Article  Google Scholar 

  15. V. Lakshmikantham, D. D. Bainov, P. S. Simeonov. Theory of Impulsive Differential Equations [M]. Singapore: World Scientific, 1989.

    MATH  Google Scholar 

  16. B. Liu, X. Liu, X. Liao. Stability and robust stability of quasi-linear impulsive hybrid dynamical systems [J]. J. of Mathematical Analysis and Application, 2003,283(7):416–430.

    Article  MATH  Google Scholar 

  17. B. Liu, X. Liu, X. Liao. Robust stability analysis of uncertain impulsive systems [J]. J. of Mathematical Analysis and Application, 2004,290 (2):519–533.

    Article  MATH  Google Scholar 

  18. . Liu, X. Liu, G. Chen, et al. Robust impulsive synchronization of uncertain dynamical networks [J]. IEEE Trans, on Circuits Systems — I, 2005, (in press).

  19. B. Liu, X. Liu, X. Liao. Robust dissipativity and feedback stabilization for interval linear impulsive dynamical systems [J]. Control Theory & Application, 2003,20(5):32–36.

    Google Scholar 

  20. B. Liu, X. Liu, X. Liao. Chaotic synchronization of general Lur’ e systems [J]. Acta Automatisa Sinica, 2004,30(1): 155–160.

    Google Scholar 

  21. G. Chen,D. Lai.Feedback control of Lyapupov exponents for discretetime dynamical systems [J]. Int. J. Bifurcation Chaos, 1996,6(10): 1341–3149. $

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, 410083, Changsha Hunan, China

    Yonghong Long & Min Wu

  2. Zhuzhou Institute of Technology, 412008, Zhuzhou Hunan, China

    Yonghong Long & Bin Liu

  3. Department of Control Science and Engineering, Huazhong University of Science and Technology, 430074, Wuhan Hubei, China

    Bin Liu

Authors
  1. Yonghong Long
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  2. Min Wu
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  3. Bin Liu
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Additional information

This work was supported by the National Natural Science Foundation of China (No. 60425310), the Excellent Young Program of the Education Department of Hunan Province (No.04B068), and the Post Doctoral Foundation of China (No. 2003034485).

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Long, Y., Wu, M. & Liu, B. Robust impulsive synchronization of linear discrete dynamical networks. J. Control Theory Appl. 3, 20–26 (2005). https://doi.org/10.1007/s11768-005-0056-8

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  • DOI: https://doi.org/10.1007/s11768-005-0056-8

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