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Exponential stability of semi-Markovian jump generalized neural networks with interval time-varying delays

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Abstract

This draft addresses the exponential stability problem for semi-Markovian jump generalized neural networks (S-MJGNNs) with interval time-varying delays. The exponential stability conditions are derived by establishing a suitable Lyapunov–Krasovskii functional and applying new analysis method. Improved results are obtained to guarantee the exponential stability of S-MJGNNs through improved reciprocally convex combination and new weighted integral inequality techniques. The method in this paper shows the advantages over some existing ones. To verify the advantages and benefits of employing proposed method is explained through numerical examples.

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References

  1. Song Q, Cao J (2012) Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dyn 67:1695–1707

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhu Q, Cao J (2012) Stability of Markovian jump neural networks with impulse control and time varying delays. Nonlinear Anal Real World Appl 13:2259–2270

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahn CK, Shi P, Wu L (2015) Receding Horizon stabilization and disturbance attenuation for neural networks with time-varying delay. IEEE Trans Cybern 45(12):2680–2692

    Article  Google Scholar 

  4. Liu Y, Ma W, Mahmoud MS (2012) New results for global exponential stability of neural networks with varying delays. Neurocomputing 97:357–363

    Article  Google Scholar 

  5. Ahn CK, Wu L, Shi P (2016) Stochastic stability analysis for 2-D Roesser systems with multiplicative noise. Automatica 69:356–363

    Article  MathSciNet  MATH  Google Scholar 

  6. Syed Ali M, Saravanakumar R, Cao J (2016) New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays. Neurocomputing 171:1533–1547

    Article  Google Scholar 

  7. Saravanakumar R, Syed Ali M, Hua M (2016) \(H_\infty\) state estimation of stochastic neural networks with mixed time-varying delays. Soft Comput. doi:10.1007/s00500-015-1901-4

  8. Wu ZG, Shi P, Su H, Chu J (2013) Dissipativity analysis for discrete-time stochastic neural networks with time-varying delays. IEEE Trans. Neural Netw Learn Syst 24(3):345–355

    Article  Google Scholar 

  9. Ahn CK (2014) \(L_2\)-\(L_\infty\) suppression of limit cycles in interfered two-dimensional digital filters: a Fornasini–Marchesini model case. IEEE Trans Circuits Syst II Exp Briefs 61(8):614–618

    Article  Google Scholar 

  10. Ahn CK, Shi P, Basin MV (2015) Two-dimensional dissipative control and filtering for Roesser model. IEEE Trans Autom Control 60(7):1745–1759

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhu Q, Cao J (2012) Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays. IEEE Trans Neural Netw Learn Syst 23(3):467–479

    Article  MathSciNet  Google Scholar 

  12. Zhu Q, Rakkiyappan R, Chandrasekar A (2014) Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control. Neurocomputing 136:136–151

    Article  Google Scholar 

  13. Rakkiyappan R, Chandrasekar A, Lakshmanan S, Park JH, Jung HY (2013) Effects of leakage time-varying delays in Markovian jump neural networks with impulse control. Neurocomputing 121:365–378

    Article  Google Scholar 

  14. Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2014) New and improved results on stability of static neural networks with interval time-varying delays. Appl Math Comput 239:346–357

    MathSciNet  MATH  Google Scholar 

  15. Liang J, Cao J (2006) A based-on LMI stability criterion for delayed recurrent neural networks. Chaos Solitons Fractals 28:154–160

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang XM, Han QL (2011) Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans Neural Netw 22(8):1180–1192

    Article  Google Scholar 

  17. Zhang CK, He Y, Jiang L, Wu QH, Wu M (2014) Delay-dependent stability criteria for generalized neural networks with two delay components. IEEE Trans Neural Netw Learn Syst 25(7):1263–1276

    Article  Google Scholar 

  18. Zeng H-B, He Y, Wu M, Xiao S-P (2015) Stability analysis of generalized neural networks with time-varying delays via a new integral inequality. Neurocomputing 161:148–154

    Article  Google Scholar 

  19. Balasubramaniam P, Lakshmanan S, Manivannan A (2012) Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays. Chaos Solitons Fractals 45:483–495

    Article  MATH  Google Scholar 

  20. Huang J, Shi Y (2013) Stochastic stability and robust stabilization of semi-Markov jump linear systems. Int J Robust Nonlinear Control 23(18):2028–2043

    Article  MathSciNet  MATH  Google Scholar 

  21. Hou Z, Luo J, Shi P, Nguang SK (2006) Stochastic stability of It differential equations with semi-Markovian jump parameters. IEEE Trans Autom Control 51(8):1383–1387

    Article  MATH  Google Scholar 

  22. Wang J, Shen H (2014) Passivity-based fault-tolerant synchronization control of chaotic neural networks against actuator faults using the semi-Markov jump model approach. Neurocomputing 143:51–56

    Article  Google Scholar 

  23. Li F, Shen H (2015) Finite-time \(H_\infty\) synchronization control for semi-Markov jump delayed neural networks with randomly occurring uncertainties. Neurocomputing 166:447–454

    Article  Google Scholar 

  24. Shen H, Park JH, Wu ZG, Zhang Z (2015) Finite-time \(H_\infty\) synchronization for complex networks with semi-Markov jump topology. Commun Nonlinear Sci Numer Simul 24:40–51

    Article  MathSciNet  Google Scholar 

  25. Wang X, Li C, Huang T, Duan S (2014) Global exponential stability of a class of memristive neural networks with time-varying delays. Neural Comput Appl 24(7):1707–1715

    Article  Google Scholar 

  26. Zhu Q, Cao J (2011) Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans Syst Man Cybern Syst 41(2):341–353

    Google Scholar 

  27. Zhu S, Luo W, Li J, Shen Y (2014) Robustness of globally exponential stability of delayed neural networks in the presence of random disturbances. Neural Comput Applic 25:743–749

    Article  Google Scholar 

  28. Chandrasekar A, Rakkiyappan R, Rihan FA, Lakshmanan S (2014) Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control. Neurocomputing 133:385–398

    Article  Google Scholar 

  29. Mahmoud MS, Xia Y (2011) Improved exponential stability analysis for delayed recurrent neural networks. J Frankl Inst 348:201–211

    Article  MathSciNet  MATH  Google Scholar 

  30. Zhu Q, Cao J, Rakkiyappan R (2015) Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays. Nonlinear Dyn 79:1085–1098

    Article  MathSciNet  MATH  Google Scholar 

  31. Gu K, Kharitonov VL, Chen J (2003) Stability of time delay systems. Birkhuser, Boston

    Book  MATH  Google Scholar 

  32. Han QL (2008) A delay decomposition approach to stability and \(H_\infty\) control of linear time-delay systems—part I stability. In: Proceedings of the 7th World congress on intelligent control and automation, Chongqing

  33. Seuret A, Gouaisbaut F (2013) Wirtinger-based integral inequality: application to time-delay systems. Automatica 49(9):2860–2866

    Article  MathSciNet  MATH  Google Scholar 

  34. Seuret A, Gouaisbaut F (2014) Complete quadratic Lyapunov functionals using Bessel-Legendre inequality. In: Proceedings of European control conference, pp 448–453

  35. Park PG, Lee WI, Lee SY (2015) Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. J Frankl Inst 352:1378–1396

    Article  MathSciNet  Google Scholar 

  36. Hien LV, Trinh H (2016) Exponential stability of time-delay systems via new weighted integral inequalities. Appl Math Comput 275:335–344

    MathSciNet  Google Scholar 

  37. Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19(5):667–675

    Article  MATH  Google Scholar 

  38. Seuret A, Gouaisbaut F, Fridman E (2013) Stability of systems with fast-varying delay using improved Wirtinger’s inequality. In: IEEE conference on decision and control, Florence, pp 946–951

  39. Liu Y, Lee SM, Kwon OM, Park JH (2015) New approach to stability criteria for generalized neural networks with interval time-varying delays. Neurocomputing 149:1544–1551

    Article  Google Scholar 

  40. Saravanakumar R, Syed Ali M, Cao J, Huang H (2016) \(H_\infty\) state estimation of generalised neural networks with interval time-varying delays. Int J Syst Sci. doi:10.1080/00207721.2015.1135359

  41. Syed Ali M, Arik S, Saravanakumar R (2015) Delay-dependent stability criteria of uncertain markovian jump neural networks with discrete interval and distributed time-varying delays. Neurocomputing 158:167–173

    Article  Google Scholar 

  42. Raja R, Zhu Q, Senthilraj S, Samidurai R (2015) Improved stability analysis of uncertain neutral type neural networks with leakage delays and impulsive effects. Appl Math Comput 266:1050–1069

    MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the Thailand Research Fund (TRF) Grant No. RSA5980019, the Higher Education Commission and Faculty of Science, Maejo University, Thailand.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, 50290, Thailand

    Grienggrai Rajchakit & R. Saravanakumar

  2. Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, 632115, India

    R. Saravanakumar

Authors
  1. Grienggrai Rajchakit
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  2. R. Saravanakumar
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Correspondence to R. Saravanakumar.

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Rajchakit, G., Saravanakumar, R. Exponential stability of semi-Markovian jump generalized neural networks with interval time-varying delays. Neural Comput & Applic 29, 483–492 (2018). https://doi.org/10.1007/s00521-016-2461-y

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  • DOI: https://doi.org/10.1007/s00521-016-2461-y

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