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Periodically Intermittent Stabilization of Delayed Neural Networks Based on Piecewise Lyapunov Functions/Functionals

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Abstract

This paper is concerned with the stabilization problem of delayed neural networks via a periodically intermittent controller. Two cases of time-varying bounded delays are considered: one is the time-varying delay without any constraints on the delay derivative, while the other is the time-varying delay with the delay derivative less than 1. For the first case, a piecewise time-invariant Lyapunov function-based method is applied, and the derived stability criterion improves an existing result. For the second case, a piecewise time-varying Lyapunov functional is introduced to establish a new stability criterion. Then, the obtained stability criteria are employed to design periodically intermittent controllers. Finally, two numerical examples are provided to illustrate the merits of the proposed approach.

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References

  1. S. Arik, An analysis of exponential stability of delayed neural networks with time varying delays. Neural Netw. 17, 1027–1031 (2004)

    Article  MATH  Google Scholar 

  2. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, PA, 1994)

    Book  MATH  Google Scholar 

  3. S. Cai, J. Hao, Q. He, Z. Liu, Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control. Phys. Lett. A 375(19), 1965–1971 (2011)

    Article  MATH  Google Scholar 

  4. W.-H. Chen, W.X. Zheng, Improved delay-dependent asymptotic stability criteria for delayed neural networks. IEEE Trans. Neural Netw. 19(12), 2154–2161 (2008)

    Article  Google Scholar 

  5. W.-H. Chen, W.X. Zheng, A new method for complete stability analysis of cellular neural networks with time delay. IEEE Trans. Neural Netw. 21(7), 1126–1139 (2010)

    Article  Google Scholar 

  6. W.-H. Chen, W.X. Zheng, Global exponential stability of impulsive neural networks with variable delay: an LMI approach. IEEE Trans. Circuits Syst. I 56(6), 1248–1259 (2009)

    Article  MathSciNet  Google Scholar 

  7. W.-H. Chen, W.X. Zheng, Robust stabilization of delayed Markovian jump systems subject to parametric uncertainties. Proceedings of the 46th IEEE conference on decision and control, New Orleans, LA, December 2007, pp. 3054–3059

  8. M. Forti, P. Nistri, D. Papini, Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Netw. 16(6), 1449–1463 (2005)

    Article  Google Scholar 

  9. Q. Gan, Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control. Neural Netw. 31(7), 12–21 (2012)

    Article  MATH  Google Scholar 

  10. P. Gawthrop, I. Loram, M. Lakie, H. Gollee, Intermittent control: a computational theory of human control. Biol. Cybern. 104(1–2), 31–51 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Gawthrop, S. Neild, D. Wagg, Semi-active damping using a hybrid control appproach. J. Intell. Mater. Syst. Struct. 23(18), 2103–2116 (2012)

    Article  Google Scholar 

  12. C. Hu, J. Yu, H. Jiang, Z. Teng, Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control. Nonlinearity 23(10), 2369–2391 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Hu, J. Yu, H. Jiang, Z. Teng, Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. Chaos 20(2), 023108 (2010)

    Article  MathSciNet  Google Scholar 

  14. H. Huang, T. Huang, X. Chen, C. Qian, Exponential stabilization of delayed recurrent neural networks: A state estimation based approach. Neural Netw. 48, 153–157 (2013)

    Article  MATH  Google Scholar 

  15. J. Huang, C. Li, Q. Han, Stabilization of delayed chaotic neural networks by periodically intermittent control. Circuits Syst. Signal Process 28(4), 567–579 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  16. T. Huang, C. Li, W. Yu, G. Chen, Synchronization of delayed chaotic systems with parameter mismatches by using intermittent linear state feedback. Nonlinearity 22(3), 569–584 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. T. Huang, C. Li, Chaotic synchronization by the intermittent feedback method. Comput. Appl. Math. 234(4), 1097–1104 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  18. T. Huang, C. Li, X. Liu, Synchronization of chaotic systems with delay using intermittent linear state feedback. Chaos 18(3), 033122 (2008)

    Article  MathSciNet  Google Scholar 

  19. C. Li, G. Feng, X. Liao, Stabilization of nonlinear systems via periodically intermittent control. IEEE Trans. Circuits Syst. II 54(11), 1019–1023 (2007)

    Article  Google Scholar 

  20. C. Li, X. Liao, T. Huang, Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17(1), 013103 (2007)

    Article  MathSciNet  Google Scholar 

  21. D. Liberzon, A.S. Morse, Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19, 59–70 (1999)

    Article  Google Scholar 

  22. J. Lu, D.W.C. Ho, Z. Wang, Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers. IEEE Trans. Neural Netw. 20(10), 1617–1629 (2009)

    Article  Google Scholar 

  23. S. Mou, H. Gao, J. Lam, A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. IEEE Trans. Neural Netw. 19(3), 532–535 (2008)

    Article  Google Scholar 

  24. L. Pan, J. Cao, Stochastic quasi-synchronization for delayed dynamical networks via intermittent control. Commun. Nonlinear Sci. Numer. Simul. 17(3), 1332–1343 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  25. V.N. Phat, H. Trinh, Exponential stabilization of neural networks with various activation functions and mixed time-varying delays. IEEE Trans. Neural Netw. 21(7), 1180–1184 (2010)

    Article  Google Scholar 

  26. Y. Shen, J. Wang, Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters. IEEE Trans. Neural Netw. 18(6), 1857–1862 (2007)

    Article  Google Scholar 

  27. W. Sun, H. Gao, O. Kaynak, Finite frequency \(H_\infty \) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2011)

    Article  Google Scholar 

  28. W. Sun, Y. Zhao, J. Li, L. Zhang, H. Gao, Active suspension control with frequency band constraints and actuator input delay. IEEE Trans. Ind. Electron. 59(1), 530–537 (2012)

    Article  Google Scholar 

  29. A. Wu, Z. Zeng, Exponential stabilization of memristive neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. 23(12), 1919–1929 (2012)

    Article  MathSciNet  Google Scholar 

  30. W. Xia, J. Cao, Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19(1), 013120 (2009)

    Article  MathSciNet  Google Scholar 

  31. S. Xu, J. Lam, A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Netw. 19, 76–83 (2006)

    Article  MATH  Google Scholar 

  32. Z. Zeng, W.X. Zheng, Multistability of neural networks with time varying delays and concave-convex characteristics. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 293–305 (2012)

    Article  Google Scholar 

  33. X. Zhao, L. Zhang, P. Shi, H.R. Karimi, Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits. IEEE Trans. Ind. Electron. 61(8), 4161–4170 (2012)

    Article  Google Scholar 

  34. X. Zhao, L. Zhang, P. Shi, M. Liu, Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)

    Article  MathSciNet  Google Scholar 

  35. X. Zhao, X. Liu, S. Yin, H. Li, Improved results on stability of continuous-time switched positive linear systems. Automatica 50(2), 614–621 (2014)

    Article  MathSciNet  Google Scholar 

  36. C. Zheng, Q. Shan, H. Zhang, Z. Wang, On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching. IEEE Trans. Neural Netw. Learn. Syst. 24(5), 800–811 (2013)

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61164016, Guangxi Natural Science Foundation (2011GXNSFA018141 & 2013GXNSFDA019003) and the Innovation Project of Guangxi Graduate Education (YCSZ2014036).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Wu-Hua Chen, Jiacheng Zhong, Zhiyong Jiang & Xiaomei Lu

  2. School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

    Wu-Hua Chen

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  1. Wu-Hua Chen
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  2. Jiacheng Zhong
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  3. Zhiyong Jiang
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  4. Xiaomei Lu
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Correspondence to Wu-Hua Chen.

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Chen, WH., Zhong, J., Jiang, Z. et al. Periodically Intermittent Stabilization of Delayed Neural Networks Based on Piecewise Lyapunov Functions/Functionals. Circuits Syst Signal Process 33, 3757–3782 (2014). https://doi.org/10.1007/s00034-014-9827-0

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  • DOI: https://doi.org/10.1007/s00034-014-9827-0

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