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Complexity
Volume 2018, Article ID 8546304, 13 pages
https://doi.org/10.1155/2018/8546304
Research Article

Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling

1Department of Mathematics, Bharathiar University, Coimbatore 641046, India
2Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
3Department of Mathematics, Anna University Regional Campus, Coimbatore 641046, India
4Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
5Department of Applied Mathematics, Kongju National University, Chungcheongnam-do 32588, Republic of Korea

Correspondence should be addressed to Yong-Ki Ma; rk.ca.ujgnok@amky

Received 13 July 2017; Accepted 14 December 2017; Published 16 January 2018

Academic Editor: Hiroki Sayama

Copyright © 2018 Rathinasamy Sakthivel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Cohen and S. Havlin, “Complex networks: structure, robustness and function,” Cambridge University Press, NY, USA, 2010. View at Publisher · View at Google Scholar
  2. K. Aihara, J.-i. Imura, and T. Ueta, Analysis and Control of Complex Dynamical Systems, Springer, Tokyo, 2015. View at MathSciNet
  3. M. J. Park, O. M. Kwon, J. H. Park, S. M. Lee, and E. J. Cha, “Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11634–11647, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. 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, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. S. Cai, X. Lei, and Z. Liu, “Outer synchronization between two hybrid-coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control,” Complexity, vol. 21, no. S2, pp. 593–605, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. B. Kaviarasan, R. Sakthivel, and Y. Lim, “Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory,” Neurocomputing, vol. 186, 2015. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Wang, L. Su, H. Shen, Z.-G. Wu, and J. H. Park, “Mixed H∞/passive sampled-data synchronization control of complex dynamical networks with distributed coupling delay,” Journal of The Franklin Institute, vol. 354, no. 3, pp. 1302–1320, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  8. X. Hao and J. Li, “Stochastic synchronization for complex dynamical networks with time-varying couplings,” Nonlinear Dynamics, vol. 80, no. 3, pp. 1357–1363, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. G. He, J.-A. Fang, W. Zhang, and Z. Li, “Synchronization of switched complex dynamical networks with non-synchronized subnetworks and stochastic disturbances,” Neurocomputing, vol. 171, pp. 39–47, 2016. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Sakthivel, M. Sathishkumar, B. Kaviarasan, and S. Marshal Anthoni, “Synchronization and state estimation for stochastic complex networks with uncertain inner coupling,” Neurocomputing, vol. 238, pp. 44–55, 2017. View at Publisher · View at Google Scholar · View at Scopus
  11. Z. Li, J.-a. Fang, T. Huang, and Q. Miao, “Synchronization of stochastic discrete-time complex networks with partial mixed impulsive effects,” Journal of The Franklin Institute, vol. 354, no. 10, pp. 4196–4214, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  12. X.-J. Li and G.-H. Yang, “Graph theory-based pinning synchronization of stochastic complex dynamical networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 2, pp. 427–437, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. W.-H. Chen, Z. Jiang, X. Lu, and S. Luo, “H∞ synchronization for complex dynamical networks with coupling delays using distributed impulsive control,” Nonlinear Analysis: Hybrid Systems, vol. 17, pp. 111–127, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Zhao, D. J. Hill, and T. Liu, “Synchronization of complex dynamical networks with switching topology: A switched system point of view,” Automatica, vol. 45, no. 11, pp. 2502–2511, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Shen, Y. Zhu, L. Zhang, and J. H. Park, “Extended dissipative state estimation for Markov jump neural networks with unreliable links,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 2, pp. 346–358, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. X. Song, Y. Men, J. Zhou, J. Zhao, and H. Shen, “Event-triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities,” Applied Mathematics and Computation, vol. 298, pp. 123–132, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z.-X. Li, J. H. Park, and Z.-G. Wu, “Synchronization of complex networks with nonhomogeneous Markov jump topology,” Nonlinear Dynamics, vol. 74, no. 1-2, pp. 65–75, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Shen, Z.-G. Wu, Z. Zhang, and J. H. Park, “Non-fragile mixed H∞/l2-l∞ synchronisation control for complex networks with Markov jumping-switching topology under unreliable communication links,” IET Control Theory & Applications, vol. 8, no. 18, pp. 2207–2218, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. Wang, T. Dong, and X. Liao, “Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies,” Neural Networks, vol. 74, pp. 52–57, 2016. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Shen, Z.-G. Wu, and J. H. Park, “Reliable mixed passive and H∞ filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures,” International Journal of Robust and Nonlinear Control, vol. 25, no. 17, pp. 3231–3251, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  21. F. Li, L. Wu, P. Shi, and C.-C. Lim, “State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties,” Automatica, vol. 51, pp. 385–393, 2015. View at Publisher · View at Google Scholar · View at Scopus
  22. K. Liang, M. Dai, H. Shen, J. Wang, Z. Wang, and B. Chen, “L2-L∞ synchronization for singularly perturbed complex networks with semi-Markov jump topology,” Applied Mathematics and Computation, vol. 321, pp. 450–462, 2018. View at Publisher · View at Google Scholar · View at MathSciNet
  23. H. Shen, F. Li, S. Xu, and V. Sreeram, “Slow state variables feedback stabilization for semi-markov jump systems with singular perturbations,” IEEE Transactions on Automatic Control, vol. pp, no. 99. View at Publisher · View at Google Scholar
  24. H. Shen, L. Su, and J. H. Park, “Reliable mixed H∞/passive control for T-S fuzzy delayed systems based on a semi-Markov jump model approach,” Fuzzy Sets and Systems, vol. 314, pp. 79–98, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  25. T. H. Lee, Q. Ma, S. Xu, and J. H. Park, “Pinning control for cluster synchronisation of complex dynamical networks with semi-Markovian jump topology,” International Journal of Control, vol. 88, no. 6, pp. 1223–1235, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. H. Shen, J. H. Park, Z.-G. Wu, and Z. Zhang, “Finite-time H∞ synchronization for complex networks with semi-Markov jump topology,” Communications in Nonlinear Science and Numerical Simulation, vol. 24, no. 1-3, pp. 40–51, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  27. Y. Zhang, Y. Shi, and P. Shi, “Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems,” Applied Mathematics and Computation, vol. 279, pp. 125–138, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  28. Y. Zhang, Y. Shi, and P. Shi, “Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 49, pp. 612–629, 2017. View at Google Scholar · View at MathSciNet
  29. R. Sakthivel, S. Santra, B. Kaviarasan, and K. Venkatanareshbabu, “Dissipative analysis for network-based singular systems with non-fragile controller and event-triggered sampling scheme,” Journal of The Franklin Institute, vol. 354, no. 12, pp. 4739–4761, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  30. W. Guan and F. Liu, “Non-fragile fuzzy dissipative static output feedback control for Markovian jump systems subject to actuator saturation,” Neurocomputing, vol. 193, pp. 123–132, 2016. View at Publisher · View at Google Scholar
  31. H. Shen, Y. Men, Z. Wu, and J. H. Park, “Nonfragile H∞ control for fuzzy markovian jump systems under fast sampling singular perturbation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. pp, no. 99, pp. 1–12. View at Publisher · View at Google Scholar
  32. Z.-G. Wu, J. H. Park, H. Su, and J. Chu, “Non-fragile synchronisation control for complex networks with missing data,” International Journal of Control, vol. 86, no. 3, pp. 555–566, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. D. Li, Z. Wang, G. Ma, and C. Ma, “Non-fragile synchronization of dynamical networks with randomly occurring nonlinearities and controller gain fluctuations,” Neurocomputing, vol. 168, pp. 719–725, 2015. View at Publisher · View at Google Scholar · View at Scopus
  34. G. Wang, L. Liu, Q. Zhang, and C. Yang, “Finite-time stability and stabilization of stochastic delayed jump systems via general controllers,” Journal of The Franklin Institute, vol. 354, no. 2, pp. 938–966, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. X. Yang, Z. Wu, and J. Cao, “Finite-time synchronization of complex networks with nonidentical discontinuous nodes,” Nonlinear Dynamics, vol. 73, no. 4, pp. 2313–2327, 2013. View at Publisher · View at Google Scholar · View at Scopus
  36. J. Mei, M. Jiang, W. Xu, and B. Wang, “Finite-time synchronization control of complex dynamical networks with time delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 9, pp. 2462–2478, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. G. Mei, X. Wu, D. Ning, and J.-A. Lu, “Finite-time stabilization of complex dynamical networks via optimal control,” Complexity, vol. 21, no. S1, pp. 417–425, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. L. Li, Z. Tu, J. Mei, and J. Jian, “Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods,” Nonlinear Dynamics, vol. 85, no. 1, pp. 375–388, 2016. View at Publisher · View at Google Scholar · View at Scopus