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Complexity
Volume 2017, Article ID 9323172, 10 pages
https://doi.org/10.1155/2017/9323172
Research Article

Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Hubei Normal University, Hubei 435002, China

Correspondence should be addressed to Jin-E Zhang; moc.361@50212068gnahz

Received 1 April 2017; Accepted 5 July 2017; Published 7 August 2017

Academic Editor: Guang Li

Copyright © 2017 Jin-E Zhang. 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. Y. Gu, Y. Yu, and H. Wang, “Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 353, no. 15, pp. 3657–3684, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. P. Liu, Z. Zeng, and J. Wang, “Multiple Mittag–Leffler Stability of Fractional-Order Recurrent Neural Networks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2279–2288, 2017. View at Publisher · View at Google Scholar
  3. R. Rakkiyappan, J. Cao, and G. Velmurugan, “Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 1, pp. 84–97, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. G. Velmurugan, R. Rakkiyappan, V. Vembarasan, J. Cao, and A. Alsaedi, “Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay,” Neural Networks, vol. 86, pp. 42–53, 2017. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Wu and Z. Zeng, “Boundedness, Mittag-Leffler stability and asymptotical ω-periodicity of fractional-order fuzzy neural networks,” Neural Networks, vol. 74, pp. 73–84, 2016. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Wu and Z. Zeng, “Global Mittag–Leffler stabilization of fractional-order memristive neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 1, pp. 206–217, 2017. View at Publisher · View at Google Scholar
  7. A. Wu, L. Liu, T. Huang, and Z. Zeng, “Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments,” Neural Networks, vol. 85, pp. 118–127, 2017. View at Publisher · View at Google Scholar
  8. J. Xiao, S. Zhong, Y. Li, and F. Xu, “Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays,” Neurocomputing, vol. 219, pp. 431–439, 2017. View at Publisher · View at Google Scholar
  9. X. Yang, C. Li, T. Huang, Q. Song, and X. Chen, “Quasi-uniform synchronization of fractional-order memristor-based neural networks with delay,” Neurocomputing, vol. 234, pp. 205–215, 2017. View at Publisher · View at Google Scholar
  10. L. Zhang, Q. Song, and Z. Zhao, “Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays,” Applied Mathematics and Computation, vol. 298, pp. 296–309, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  11. L. Zhang, Y. Yang, and F. Wang, “Projective synchronization of fractional-order memristive neural networks with switching jumps mismatch,” Physica A. Statistical Mechanics and its Applications, vol. 471, pp. 402–415, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  12. W. Zhou, X. Zhou, J. Yang, Y. Liu, X. Zhang, and X. Ding, “Exponential synchronization for stochastic neural networks driven by fractional Brownian motion,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 353, no. 8, pp. 1689–1712, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. C. D. Cruz-Ancona, R. Martínez-Guerra, and C. A. Pérez-Pinacho, “Generalized multi-synchronization: a leader-following consensus problem of multi-agent systems,” Neurocomputing, vol. 233, pp. 52–60, 2017. View at Publisher · View at Google Scholar · View at Scopus
  14. R. Martinez-Guerra, C. D. Cruz-Ancona, and C. A. Perez-Pinacho, “Generalized multi-synchronization viewed as a multi-agent leader-following consensus problem,” Applied Mathematics and Computation, vol. 282, pp. 226–236, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  15. H. Salarieh and M. Shahrokhi, “Multi-synchronization of chaos via linear output feedback strategy,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 842–852, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. Y.-W. Wang, W. Yang, J.-W. Xiao, and Z.-G. Zeng, “Impulsive multisynchronization of coupled multistable neural networks with time-varying delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 7, pp. 1560–1571, 2017. View at Google Scholar
  17. X. Yang, J. Cao, and J. Lu, “Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 2, pp. 371–384, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  18. W. Zhang, Y. Tang, Q. Miao, and J.-A. Fang, “Synchronization of stochastic dynamical networks under impulsive control with time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 10, pp. 1758–1768, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. M. Ayati and H. Khaloozadeh, “Designing a novel adaptive impulsive observer for nonlinear continuous systems using {LMI}s,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 1, pp. 179–187, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. W.-H. Chen, D. Wei, and W. X. Zheng, “Delayed impulsive control of takagi-sugeno fuzzy delay systems,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 3, pp. 516–526, 2013. View at Publisher · View at Google Scholar · View at Scopus
  21. Y. Chen, W. Yu, F. Li, and S. Feng, “Synchronization of complex networks with impulsive control and disconnected topology,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 60, no. 5, pp. 292–296, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Claeys, D. Arzelier, D. Henrion, and J.-B. Lasserre, “Measures and {LMI}s for impulsive nonlinear optimal control,” IEEE Transactions on Automatic ControL, vol. 59, no. 5, pp. 1374–1379, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  23. L. Ding, P. Yu, Z.-W. Liu, and Z.-H. Guan, “Consensus and performance optimisation of multi-agent systems with position-only information via impulsive control,” IET Control Theory & Applications, vol. 7, no. 1, pp. 16–24, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  24. W. Du, S. Y. S. Leung, Y. Tang, and A. V. Vasilakos, “Differential evolution with event-triggered impulsive control,” IEEE Transactions on Cybernetics, vol. 47, no. 1, pp. 244–257, 2017. View at Publisher · View at Google Scholar · View at Scopus
  25. S. L. Fraga and F. L. Pereira, “Hamilton-Jacobi-Bellman equation and feedback synthesis for impulsive control,” IEEE Transactions on Automatic Control, vol. 57, no. 1, pp. 244–249, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  26. D. He and L. Xu, “Ultimate Boundedness of Nonautonomous Dynamical Complex Networks under Impulsive Control,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 62, no. 10, pp. 997–1001, 2015. View at Publisher · View at Google Scholar · View at Scopus
  27. X. Li and S. Song, “Stabilization of Delay Systems: delay-dependent Impulsive Control,” IEEE Transactions on Automatic Control, vol. 62, no. 1, pp. 406–411, 2017. View at Publisher · View at Google Scholar
  28. Y. Li, Y. Sun, J. Hua, and L. Li, “Indirect adaptive type-2 fuzzy impulsive control of nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 23, no. 4, pp. 1084–1099, 2015. View at Publisher · View at Google Scholar · View at Scopus
  29. X. Liu and K. Zhang, “Impulsive control for stabilisation of discrete delay systems and synchronisation of discrete delay dynamical networks,” IET Control Theory & Applications, vol. 8, no. 13, pp. 1185–1195, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  30. Y. Liu, S. Zhao, and J. Lu, “A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 393–398, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. X. Lu, N. Chen, Y. Wang, L. Qu, and J. Lai, “Distributed impulsive control for islanded microgrids with variable communication delays,” IET Control Theory & Applications, vol. 10, no. 14, pp. 1732–1739, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  32. T. H. Cormen, C. E. Leiserson, R. Rivest, and C. Stein, Introduction to Algorithms, The MIT Press, Cambridge, Massachusetts, Mass, USA, 2009. View at MathSciNet
  33. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, USA, 1994.
  34. A. Wu and Z. Zeng, “Output convergence of fuzzy neurodynamic system with piecewise constant argument of generalized type and time-varying input,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 12, pp. 1689–1702, 2016. View at Publisher · View at Google Scholar