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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 6157292, 10 pages
https://doi.org/10.1155/2017/6157292
Research Article

Centralized Data-Sampling Approach for Global Synchronization of Fractional-Order Neural Networks with Time Delays

Hubei Normal University, Hubei 435002, China

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

Received 8 November 2016; Revised 18 December 2016; Accepted 9 January 2017; Published 9 February 2017

Academic Editor: Qasem M. Al-Mdallal

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. I. Ameen and P. Novati, “The solution of fractional order epidemic model by implicit Adams methods,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 43, pp. 78–84, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  2. 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
  3. B. S. Chen and J. J. Chen, “Global O(tα) stability and global asymptotical periodicity for a non-autonomous fractional-order neural networks with time-varying delays,” Neural Networks, vol. 73, pp. 47–57, 2016. View at Google Scholar
  4. J. Palanivel, K. Suresh, S. Sabarathinam, and K. Thamilmaran, “Chaos in a low dimensional fractional order nonautonomous nonlinear oscillator,” Chaos, Solitons & Fractals, vol. 95, pp. 33–41, 2017. View at Publisher · View at Google Scholar
  5. N. Miljković, N. Popović, O. Djordjević, L. Konstantinović, and T. B. Šekara, “ECG artifact cancellation in surface EMG signals by fractional order calculus application,” Computer Methods and Programs in Biomedicine, vol. 140, pp. 259–264, 2017. View at Publisher · View at Google Scholar
  6. S. Saha Ray and S. Sahoo, “Two efficient reliable methods for solving fractional fifth order modified Sawada–Kotera equation appearing in mathematical physics,” Journal of Ocean Engineering and Science, vol. 1, no. 3, pp. 219–225, 2016. View at Publisher · View at Google Scholar
  7. K. Amoura, R. Mansouri, M. Bettayeb, and U. M. Al-Saggaf, “Closed-loop step response for tuning PID-fractional-order-filter controllers,” ISA Transactions, vol. 64, pp. 247–257, 2016. View at Publisher · View at Google Scholar · View at Scopus
  8. R. Rakkiyappan, G. Velmurugan, and J. Cao, “Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays,” Nonlinear Dynamics, vol. 78, no. 4, pp. 2823–2836, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. Rakkiyappan, G. Velmurugan, and J. Cao, “Stability analysis of memristor-based fractional-order neural networks with different memductance functions,” Cognitive Neurodynamics, vol. 9, no. 2, pp. 145–177, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Rakkiyappan, G. Velmurugan, and J. Cao, “Stability analysis of fractional-order complex-valued neural networks with time delays,” Chaos, Solitons and Fractals, vol. 78, pp. 297–316, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. D. K. Raju, B. S. Umre, A. Junghare, and B. C. Babu, “Mitigation of subsynchronous resonance with fractional-order PI based UPFC controller,” Mechanical Systems and Signal Processing, vol. 85, pp. 698–715, 2017. View at Publisher · View at Google Scholar
  12. F. Wang, Y. Yang, M. Hu, and X. Xu, “State estimation for fractional-order neural networks,” Optik, vol. 126, no. 23, pp. 4083–4086, 2015. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Arya and N. Kumar, “BFOA-scaled fractional order fuzzy PID controller applied to AGC of multi-area multi-source electric power generating systems,” Swarm and Evolutionary Computation, vol. 32, pp. 202–218, 2017. View at Publisher · View at Google Scholar
  14. 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
  15. G. M. Mahmoud, M. E. Ahmed, and T. M. Abed-Elhameed, “On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization,” Optik, vol. 130, pp. 398–406, 2017. View at Publisher · View at Google Scholar
  16. A. Wu, Z. Zeng, and X. Song, “Global Mittag-Leffler stabilization of fractional-order bidirectional associative memory neural networks,” Neurocomputing, vol. 177, pp. 489–496, 2016. View at Publisher · View at Google Scholar · View at Scopus
  17. R. Sharma, P. Gaur, and A. P. Mittal, “Design of two-layered fractional order fuzzy logic controllers applied to robotic manipulator with variable payload,” Applied Soft Computing, vol. 47, pp. 565–576, 2016. View at Publisher · View at Google Scholar · View at Scopus
  18. J. A. Gallegos and M. A. Duarte-Mermoud, “On the Lyapunov theory for fractional order systems,” Applied Mathematics and Computation, vol. 287- 288, pp. 161–170, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. S. Zhang, Y. Yu, and H. Wang, “Mittag-Leffler stability of fractional-order Hopfield neural networks,” Nonlinear Analysis. Hybrid Systems, vol. 16, pp. 104–121, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. Q.-L. Han, “A discrete delay decomposition approach to stability of linear retarded and neutral systems,” Automatica, vol. 45, no. 2, pp. 517–524, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. Y. He, J. Zeng, M. Wu, and C.-K. Zhang, “Robust stabilization and H controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties,” Mathematical Biosciences, vol. 236, no. 1, pp. 53–63, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. Huang, T. Huang, and X. Chen, “Global exponential estimates of delayed stochastic neural networks with Markovian switching,” Neural Networks, vol. 36, pp. 136–145, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  23. J. Liang, Z. Wang, Y. Liu, and X. Liu, “State estimation for two-dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays,” International Journal of Robust and Nonlinear Control, vol. 24, no. 1, pp. 18–38, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  24. D. Liu and Q. Wei, “Finite-approximation-error-based optimal control approach for discrete-time nonlinear systems,” IEEE Transactions on Cybernetics, vol. 43, no. 2, pp. 779–789, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Lu, D. W. Ho, J. Cao, and J. Kurths, “Single impulsive controller for globally exponential synchronization of dynamical networks,” Nonlinear Analysis. Real World Applications, vol. 14, no. 1, pp. 581–593, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. 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
  27. R. Wang, P. Shi, Z.-G. Wu, and Y.-T. Sun, “Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching,” Journal of the Franklin Institute, vol. 350, no. 8, pp. 2028–2043, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. Z. Wang, B. Shen, H. Shu, and G. Wei, “Quantized H control for nonlinear stochastic time-delay systems with missing measurements,” Institute of Electrical and Electronics Engineers. Transactions on Automatic Control, vol. 57, no. 6, pp. 1431–1444, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. Z. Wang, H. Zhang, and B. Jiang, “LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures,” IEEE Transactions on Neural Networks, vol. 22, no. 7, pp. 1032–1045, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. H. G. Zhang, Z. S. Wang, and D. Liu, “A comprehensive review of stability analysis of continuous-time recurrent neural networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 7, pp. 1229–1262, 2014. View at Publisher · View at Google Scholar · View at Scopus
  31. H. Li, “Event-triggered state estimation for a class of delayed recurrent neural networks with sampled-data information,” Abstract and Applied Analysis, vol. 2012, Article ID 731453, 21 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. M. Abdelrahim, R. Postoyan, J. Daafouz, and D. Nesic, “Robust event-triggered output feedback controllers for nonlinear systems,” Automatica, vol. 75, pp. 96–108, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  33. A. Tanwani, C. Prieur, and M. Fiacchini, “Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization,” Systems and Control Letters, vol. 94, pp. 46–56, 2016. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  34. A. Seuret, C. Prieur, S. Tarbouriech, and L. Zaccarian, “Event-triggered control via reset control systems framework,” IFAC-PapersOnLine, vol. 49, no. 18, pp. 170–175, 2016. View at Publisher · View at Google Scholar
  35. N. K. Sharma and T. V. Sreenivas, “Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation,” Signal Processing, vol. 116, pp. 43–54, 2015. View at Publisher · View at Google Scholar · View at Scopus
  36. S. Dashkovskiy and S. Pavlichkov, “Constructive design of adaptive controllers for nonlinear MIMO systems with arbitrary switchings,” IEEE Transactions on Automatic Control, vol. 61, no. 7, pp. 2001–2007, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. A. A. Pyrkin and A. A. Bobtsov, “Adaptive controller for linear system with input delay and output disturbance,” in Proceedings of the 52nd IEEE Conference on Decision and Control (CDC '13), vol. 61, pp. 4229–4234, IEEE, Florence, Italy, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  38. J. E. Azzaro and R. A. Veiga, “Sliding mode controller with neural network identification,” IEEE Latin America Transactions, vol. 13, no. 12, pp. 3754–3757, 2015. View at Publisher · View at Google Scholar