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Global Exponential Stability of Hybrid Non-autonomous Neural Networks with Markovian Switching

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Abstract

This paper discusses the global exponential stability for a class of hybrid non-autonomous neural networks (HNNNs) with Markovian switching, which includes the factors of time delays and impulse disturbance. A novel Halanay inequality with cross terms is established by using stochastic analysis technique. Some sufficiency criteria for the global exponential stability of the HNNNs with Markovian switching are derived by the Halanay inequality and some mathematical analysis methods. The results obtained have better fault tolerance and redundancy under certain accuracy than the existing results in the literature. Finally, numerical experiments are provided to illustrate our theoretical results.

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References

  1. Nazemi A (2018) A capable neural network framework for solving degenerate quadratic optimization problems with an application in image fusion. Neural Process Lett 47(1):167–192

    Google Scholar 

  2. Liu Z, Xiao B, Alrabeiah M et al (2019) Single image dehazing with a generic model-agnostic convolutional neural network. IEEE Signal Process Lett 26(6):833–837

    Google Scholar 

  3. Chang P, Zhang J, Hu J et al (2018) A deep neural network based on ELM for semi-supervised learning of image classification. Neural Process Lett 48(1):375–388

    Google Scholar 

  4. Trentin E, Schwenker F, Gayar NE et al (2018) Off the mainstream: advances in neural networks and machine learning for pattern recognition. Neural Process Lett 48(2):643–648

    Google Scholar 

  5. Yang J, Wang L, Wang Y et al (2017) A novel memristive Hopfield neural network with application in associative memory. Neurocomputing 227:142–148

    Google Scholar 

  6. Hu B, Guan Z, Chen G et al (2019) Multistability of delayed hybrid impulsive neural networks with application to associative memories. IEEE Trans Neural Netw Learn Syst 30(5):1537–1551

    MathSciNet  Google Scholar 

  7. Nazemi A, Karami R (2017) A neural network approach for solving optimal control problems with inequality constraints and some applications. Neural Process Lett 45(3):995–1023

    Google Scholar 

  8. Qin S, Xue X (2015) A two-layer recurrent neural network for nonsmooth convex optimization problems. IEEE Trans Neural Netw Learn Syst 26(6):1149–1160

    MathSciNet  Google Scholar 

  9. Uykan Z (2013) Fast-convergent double-sigmoid Hopfield neural network as applied to optimization problems. IEEE Trans Neural Netw Learn Syst 24(6):990–996

    Google Scholar 

  10. Li C, Yu X, Huang T et al (2016) A generalized Hopfield network for nonsmooth constrained convex optimization: lie derivative approach. IEEE Trans Neural Netw Learn Syst 27(2):308–321

    MathSciNet  Google Scholar 

  11. Li X, Song S (2013) Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learn Syst 24(6):868–877

    Google Scholar 

  12. Wang Z, Guo Z, Huang L et al (2017) Dynamical behavior of complex-valued Hopfield neural networks with discontinuous activation functions. Neural Process Lett 45(3):1039–1061

    Google Scholar 

  13. Rathinasamy A, Narayanasamy J (2019) Mean square stability and almost sure exponential stability of two step Maruyama methods of stochastic delay Hopfield neural networks. Appl Math Comput 348:126–152

    MathSciNet  MATH  Google Scholar 

  14. Syed Ali M, Yogambigai J (2017) Exponential stability of semi-Markovian switching complex dynamical networks with mixed time varying delays and impulse control. Neural Process Lett 46(1):113–133

    Google Scholar 

  15. Liu L, Zhu Q, Feng L (2018) Lagrange stability for delayed recurrent neural networks with Markovian switching based on stochastic vector Halandy inequalities. Neurocomputing 275:1614–1621

    Google Scholar 

  16. Li D, Ma C (2014) Attractor and stochastic boundedness for stochastic infinite delay neural networks with Markovian switching. Neural Process Lett 40(2):127–142

    Google Scholar 

  17. Liu L, Cao J, Qian C (2018) \(p\)th moment exponential input-to-State stability of delayed recurrent neural networks With Markovian switching via vector Lyapunov function. IEEE Trans Neural Netw Learn Syst 29(7):3152–3163

    MathSciNet  Google Scholar 

  18. Feng L, Cao J, Liu L (2019) Stability analysis in a class of Markov switched stochastic Hopfield neural networks. Neural Process Lett 50(1):413–430

    Google Scholar 

  19. Maharajan C, Raja R, Cao J et al (2019) Fractional delay segments method on time-delayed recurrent neural networks with impulsive and stochastic effects: an exponential stability approach. Neurocomputing 323:277–298

    Google Scholar 

  20. Shu Y, Liu XG, Qiu S et al (2017) Dissipativity analysis for generalized neural networks with Markovian jump parameters and time-varying delay. Nonlinear Dyn 89(3):2125–2140

    MathSciNet  MATH  Google Scholar 

  21. Wang P, Wang X, Su H (2019) Stability analysis for complex-valued stochastic delayed networks with Markovian switching and impulsive effects. Commun Nonlinear Sci Numer Simul 73:35–51

    MathSciNet  Google Scholar 

  22. Xie D, Jiang Y, Han M (2018) Global exponential synchronization of complex-valued neural networks with time delays via matrix measure method. Neural Process Lett 49(1):187–201

    Google Scholar 

  23. Li L, Shi X, Liang J (2019) Synchronization of impulsive coupled complex-valued neural networks with delay: the matrix measure method. Neural Netw 117:285–294

    MATH  Google Scholar 

  24. Zheng CD, Zhang H, Wang Z (2014) Exponential synchronization of stochastic chaotic neural networks with mixed time delays and Markovian switching. Neural Comput Appl 25(2):429–442

    Google Scholar 

  25. Wei Y, Park JH, Karimi HR et al (2017) Improved stability and stabilization results for stochastic synchronization of continuous-time semi-Markovian jump neural networks with time-varying delay. IEEE Trans Neural Netw Learn Syst 29(6):2488–2501

    MathSciNet  Google Scholar 

  26. Li R, Cao J (2016) Finite-time stability analysis for Markovian jump memristive neural networks with partly unknown transition probabilities. IEEE Trans Neural Netw Learn Syst 28(12):2924–2935

    MathSciNet  Google Scholar 

  27. Van Hien L, Son DT, Trinh H (2018) On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE Trans Neural Netw Learn Syst 29(1):225–231

    MathSciNet  Google Scholar 

  28. Shen H, Wang T, Cao J et al (2018) Nonfragile dissipative synchronization for Markovian memristive neural networks: a gain-scheduled control scheme. IEEE Trans Neural Netw Learn Syst 30(6):1841–1853

    MathSciNet  Google Scholar 

  29. Samidurai R, Manivannan R, Ahn CK et al (2016) New criteria for stability of generalized neural networks including Markov jump parameters and additive time delays. IEEE Trans Neural Netw Learn Syst 48(4):485–499

    Google Scholar 

  30. Liu L, He X, Wu A (2019) \(p\)th moment exponential input-to-state stability of non-autonomous delayed Cohen-Grossberg neural networks with Markovian switching. Neurocomputing 349:44–51

    Google Scholar 

  31. Li Z, Liu L, Zhu Q (2016) Mean-square exponential input-to-state stability of delayed Cohen–Grossberg neural networks with Markovian switching based on vector Lyapunov functions. Neural Netw 84:39–46

    MATH  Google Scholar 

  32. Zhao H, Li L, Peng H et al (2018) Finite-time robust synchronization of memrisive neural network with perturbation. Neural Process Lett 47(2):509–533

    Google Scholar 

  33. Wan X, Yang X, Tang R et al (2019) Exponential synchronization of semi-Markovian coupled neural networks with mixed delays via tracker information and quantized output controller. Neural Netw 118:321–331

    MATH  Google Scholar 

  34. Baskar P, Padmanabhan S, Ali MS (2018) Finite-time Hontrol control for a class of Markovian jumping neural networks with distributed time varying delays-LMI approach. Acta Mathematica Scientia 38(2):561–579

    MathSciNet  MATH  Google Scholar 

  35. Li X (2019) Global exponential stability of impulsive delay systems with flexible impulse frequency. IEEE Trans Syst Man Cybern Syst 49(10):2166–2174

    Google Scholar 

  36. Rakkiyappan R, Chandrasekar A, Lakshmanan S et al (2014) Exponential stability of Markovian jumping stochastic CohenCGrossberg neural networks with mode-dependent probabilistic time-varying delays and impulses. Neurocomputing 131:265–277

    Google Scholar 

  37. Wang Z, Liu X (2019) Exponential stability of impulsive complex-valued neural networks with time delay. Math Comput Simul 156:143–157

    MathSciNet  Google Scholar 

  38. Cao Y, Wang S, Guo Z et al (2019) Synchronization of memristive neural networks with leakage delay and parameters mismatch via event-triggered control. Neural Netw 119:178–189

    MATH  Google Scholar 

  39. Wang FX, Liu XG, Li J (2018) Synchronization analysis for fractional non-autonomous neural networks by a Halanay inequality. Neurocomputing 314:20–29

    Google Scholar 

  40. Son DT, Trinh H (2018) On global dissipativity of nonautonomous neural networks with multiple proportional delays. IEEE Trans Neural Netw Learn Syst 29(1):225–231

    MathSciNet  Google Scholar 

  41. Syed Ali M, Yogambigai J (2019) Synchronization criterion of complex dynamical networks with both leakage delay and coupling delay on time scales. Neural Process Lett 49(2):453–466

    Google Scholar 

  42. Zhou L, Liu X (2017) Mean-square exponential input-to-state stability of stochastic recurrent neural networks with multi-proportional delays. Neurocomputing 219:396–403

    Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Key Program) under Grant 61836010. The authors would like to thank their laboratory team member’s assistance.

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Authors and Affiliations

  1. Department of Electronic Engineering, School of Electronic Science and Engineering, Xiamen University, Xiamen, 361005, China

    Chenhui Zhao & Donghui Guo

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  1. Chenhui Zhao
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  2. Donghui Guo
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Correspondence to Chenhui Zhao.

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Zhao, C., Guo, D. Global Exponential Stability of Hybrid Non-autonomous Neural Networks with Markovian Switching. Neural Process Lett 52, 525–543 (2020). https://doi.org/10.1007/s11063-020-10262-3

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