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Quasi-synchronization of Markovian jump complex heterogeneous networks with partly unknown transition rates

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Abstract

This paper is concerned with the synchronization problem for a class of Markovian jump complex heterogeneous networks with partly unknown transition rates and time-varying delay. Based on the concept of quasi-synchronization, a novel stochastic Lyapunov functional is constructed to solve the problem. Then sufficient quasi-synchronization conditions are presented, and explicit expressions of error levels are proposed to estimate the synchronization error. Finally, numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed theoretic result.

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References

  1. A. Arenas, A. Diaz-Guilera, and C. Perez-Vicente, “Synchronization processes in complex networks,” Physica D: Nonlinear Phenomena, vol. 224, no. 1–2, pp. 27–34, December 2006.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Liang, Z. Wang, and X. Liu, “Exponential synchronization of stochastic delayed discrete-time complex networks,” Nonlinear Dynamics, vol. 53, no. 1–2, pp. 153–165, July 2008.

    Article  MATH  MathSciNet  Google Scholar 

  3. Y. Liu, Z. Wang, J. Liang, and X. Liu, “Synchronization and state estimation for discrete-time complex networks with distributed delays,” IEEE Trans. on Systems, Man and Cybernetics, vol. 38, no. 5, pp. 1314–1325, October 2008.

    Article  MathSciNet  Google Scholar 

  4. Z. Wang, Y. Wang, and Y. Liu, “Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays,” IEEE Trans. on Neural Networks, vol. 21, no. 1, pp. 11–25, January 2010.

    Article  Google Scholar 

  5. D. Yue and H. Li, “Synchronization stability of continuous/discrete complex dynamical networks with interval time-varying delays,” Neurocomputing, vol. 73, no. 4–6, pp. 809–819, January 2010.

    Article  Google Scholar 

  6. C. F. Fan, F. W. Yang, and Y. Zhou, “State estimation for coupled output discrete-time complex network with stochastic measurements and different inner coupling matrices,” International Journal of Control, Automation, and Systems, vol. 10, no. 3, pp. 498–505, June 2012.

    Article  Google Scholar 

  7. J. W. Yi, Y. W. Wang, J. W. Xiao, and Y. H. Huang, “Exponential synchronization of complex dynamical networks with Markovian jump parameters and stochastic delays and its application to multi-agent systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 5, pp. 1175–1192, May 2013.

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. Zheng, Y. Zhu, and L. Wang, “Consensus of heterogeneous multi-agent systems,” IET Control Theory and Applications, vol. 5, no. 16, pp. 1881–1888, April 2011.

    Article  MathSciNet  Google Scholar 

  9. G. Vogel, “Team claims success with cow-mouse nuclear transfer,” Science, vol. 313, no. 5784, pp. 155–156, July 2006.

    Google Scholar 

  10. M. Begon, C. Townsend, and J. Harper, Ecology: Individuals, Populations and Communities, Blackwell Science, London, 1996.

    Google Scholar 

  11. J. Wang, J. Zhang, Z. Yuan, A. Chen, and T. Zhou, “Neurotransmitter-mediated collective rhythms in grouped drosophila circadian clocks,” Journal of Biological Rhythms, vol. 23, no. 6, pp. 472–482, December 2008.

    Article  Google Scholar 

  12. Q. Song, J. Cao, and F. Liu, “Synchronization of complex dynamical networks with nonidentical nodes,” Physics Letters A, vol. 374, no. 4, pp. 544–551, January 2010.

    Article  MATH  Google Scholar 

  13. Z. Duan and G. Chen, “Global robust stability and synchronization of networks with Lorenz-type nodes,” IEEE Trans. on Circuits and Systems II, vol. 56, no. 8, pp. 678–683, August 2009.

    MathSciNet  Google Scholar 

  14. T. H. Lee, J. H. Park, D. H. Ji, O. M. Kwon, and S. M. Lee, “Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control,” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6469–6481, February 2012.

    Article  MATH  MathSciNet  Google Scholar 

  15. T. H. Lee, Z. G. Wu, and J. H. Park, “Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control,” Applied Mathematics and Computation, vol. 219, no. 3, pp. 1354–1366, October 2012.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Zhao, D. Hill, and T. Liu, “Stability of dynamical networks with non-identical nodes: a multiple VLyapunov function method,” Automatica, vol. 47, no. 12, pp. 2615–2625, December 2011.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Zhao, D. Hill, and T. Liu, “Global synchronization of complex dynamical networks with nonidentical nodes,” Proc. of the 26th Conf. Decision and Control, Cancun, pp. 817–822, December 2008.

    Google Scholar 

  18. Q. Ma, S. Y. Xu, and Y. Zou, “Stability and synchronization for Markovian neural networks with partly unknown transition probabilities,” Neurocomputing, vol. 74, no. 17, pp. 3404–3411, October 2011.

    Article  Google Scholar 

  19. L. P. Wang, J. Zhu, and J. Park, “A probabilistic approach for model following of Markovian jump linear systems subject to actuator saturation,” International Journal of Control, Automation, and Systems, vol. 10, no. 5, pp. 1042–1048, October 2012.

    Article  Google Scholar 

  20. T. H. Lee, S. Lakshmanan, J. H. Park, and P. Balasubramaniam, “State estimation for genetic regulatory networks with mode-dependent leakage delays, time-varying delays, and Markovian jumping parameters,” IEEE Trans. on NanoBioscience, vol. 12 no. 4, pp. 363–375, December 2013.

    Article  Google Scholar 

  21. Y. Liu, Z. Wang, J. Liang, and X. Liu, “Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays,” IEEE Trans. on Neural Network, vol. 20, no. 7, pp. 1102–1116, July 2009.

    Article  Google Scholar 

  22. Y. Liu, Z. Wang, and X. Liu, “Exponential synchronization of complex networks with Markovian jump and mixed delays,” Physics Letters A, vol. 372, no. 22, pp. 3986–3998, May 2008.

    Article  MATH  MathSciNet  Google Scholar 

  23. Y. Tang, J. Fang, and Q. Y. Miao, “Synchronization of stochastic delayed neural networks with Markovian switching and its application,” International Journal of Neural Systems, vol. 19, no. 1, pp. 43–56, February 2009.

    Article  MathSciNet  Google Scholar 

  24. Y. Tang, J. Fang, and Q. Y. Miao, “On the exponential synchronization of stochastic jumping chaotic neural networks with mixed delays and sector-bounded nonlinearities,” Neurocomputing, vol. 72, no. 7, pp. 1694–1701, March 2009.

    Article  Google Scholar 

  25. G. L. Wang, “Robust stabilization of singular Markovian jump systems with uncertain switching,” International Journal of Control, Automation, and Systems, vol. 11, no. 1, pp. 188–193, February 2013.

    Article  Google Scholar 

  26. X. Liu and H. Xi, “Exponential synchronization for neutral complex dynamical networks with interval mode-dependent delays and sampled data,” Mathematical Problems in Engineering, vol. 2013, Article ID 639580, 21 pages, October 2013.

  27. M. K. Song, J. B. Park, and Y. H. Joo, “Stability and stabilization for discrete-time Markovian jump fuzzy systems with time-varying delays: partially known transition probabilities case,” International Journal of Control, Automation, and Systems, vol. 11, no. 1, pp. 136–146, February 2013.

    Article  Google Scholar 

  28. W. Lu and T. Chen, “New approach to synchronization analysis of linearly coupled ordinary differential systems,” Physica D, vol. 213, no. 2, pp. 214–230, January 2006.

    Article  MATH  MathSciNet  Google Scholar 

  29. J. Lu and D. W. C. Ho, “Globally exponential synchronization and synchronizability for general dynamical networks,” IEEE Trans. on Systems, Man, and Cybernetics, vol. 40, no. 2, pp. 350–361, April 2010.

    Article  Google Scholar 

  30. X. Mao, “Stability of stochastic differential equations with Markovian switching,” Stochastic Processes and Their Applications, vol. 79, no. 1, pp. 45–67, January 1999.

    Article  MATH  MathSciNet  Google Scholar 

  31. W. L. He, W. L. Du, and J. D. Cao, “Synchronization analysis of heterogeneous dynamical networks,” Neurocomputing, vol. 104, no. 1, pp. 146–154, March 2013.

    Article  Google Scholar 

  32. L. V. Hien and V. N. Phat, “Exponential stabilization for a class of hybrid systems with mixed delays in state and control,” Nonlinear Analysis: Hybrid systems, vol. 3, no. 3, pp. 259–265, August 2009.

    MATH  MathSciNet  Google Scholar 

  33. X. Liu and H. Xi, “On exponential stability for a class of uncertain neutral Markovian jump systems with mode-dependent delays,” Abstract and Applied Analysis, vol. 2013, Article ID 691650, 23 pages, December 2013.

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Authors and Affiliations

  1. Department of Automation, University of Science and Technology of China, Hefei, China

    Xinghua Liu & Hongsheng Xi

Authors
  1. Xinghua Liu
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  2. Hongsheng Xi
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Correspondence to Xinghua Liu.

Additional information

Recommended by Editor Ju Hyun Park.

This work was supported in part by the National Key Scientific Research Project (61233003), the National Natural Science Foundation of China (61074033), the Doctoral Fund Ministry Education of China, (20093402110019) and the Fundamental Research Funds for the Central Universities.

Xinghua Liu received his bachelor degree from Computational Mathematics of Math College, Jilin University in 2009. In his undergraduate study, he got the scholarship for four consecutive years and took charge of a College Students’ Innovative Plan. Now he is a Ph.D. Candidate in University of Science and Technology of China (USTC). In his postgraduate stage, his research interests include hybrid systems, complex networks, stochastic estimation and control.

Hongsheng Xi received his B.S. and M.S. degrees in Applied Mathematics from University of Science and Technology of China (USTC), Hefei, China, in 1980 and 1985, respectively. He is currently the Dean of the School of Information Science and Technology, USTC. He also directs the Laboratory of Network Communication System and Control. His research interests include stochastic control systems, discreteevent dynamic systems, network performance analysis and optimization, and wireless communications.

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Liu, X., Xi, H. Quasi-synchronization of Markovian jump complex heterogeneous networks with partly unknown transition rates. Int. J. Control Autom. Syst. 12, 1336–1344 (2014). https://doi.org/10.1007/s12555-014-0078-4

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  • DOI: https://doi.org/10.1007/s12555-014-0078-4

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