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An improved delay-partitioning approach to stability criteria for generalized neural networks with interval time-varying delays

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Abstract

This paper deals with the problem of stability analysis for generalized delayed neural networks with interval time-varying delays based on the delay-partitioning approach. By constructing a suitable Lyapunov–Krasovskii functional with triple- and four-integral terms and using Jensen’s inequality, Wirtinger-based single- and double-integral inequality technique and linear matrix inequalities (LMIs), which guarantees asymptotic stability of addressed neural networks. This LMI can be easily solved via convex optimization algorithm. The novelty of this paper is that the consideration of a new integral inequalities and Lyapunov–Krasovskii functional is shown to be less conservatism, and it takes fully the relationship between the terms in the Leibniz–Newton formula within the framework of LMIs. Moreover, it is assumed that the lower bound of the time-varying delay is not restricted to be zero. Finally, several interesting numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over well-known examples existing in recent literature.

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References

  1. Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. Society for Industrial and Applied Mathematics, Philadelphia, PA

    Book  MATH  Google Scholar 

  2. Arik S (2000) Global asymptotic stability of a class of dynamical neural networks. IEEE Trans Circuits Syst I Fundam Theory Appl 47:568–571

    Article  MathSciNet  MATH  Google Scholar 

  3. Luan X, Liu F, Shi P (2010) \(H_\infty\) filtering for nonlinear systems via neural networks. J Franklin Inst 347:1035–1046

    Article  MathSciNet  MATH  Google Scholar 

  4. Cao J, Huang D-S, Qu Y (2005) Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals 23:221–229

    Article  MathSciNet  MATH  Google Scholar 

  5. Cao J, Ho Daniel WC, Huang X (2007) LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay. Nonlinear Anal 66:1558–1572

    Article  MathSciNet  MATH  Google Scholar 

  6. Gupta MM, Jin L, Homma N (2003) Static and dynamic neural networks: from fundamentals to advanced theory. Wiley, New York

    Book  Google Scholar 

  7. Li X, Fu X (2013) Effect of leakage time-varying delay on stability of nonlinear differential systems. J Franklin Inst 350:1335–1344

    Article  MathSciNet  MATH  Google Scholar 

  8. Li X, Wu J (2016) Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica 64:63–69

    Article  MathSciNet  MATH  Google Scholar 

  9. Gao H, Chen T, Lam J (2008) A new delay system approach to network-based control. Automatica 44:39–52

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang L, Boukas EK, Lam J (2008) Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Trans Autom Control 53:2458–2464

    Article  MathSciNet  MATH  Google Scholar 

  11. Li H, Zhou Q, Chen B, Liu H (2011) Parameter-dependent robust stability for uncertain Markovian jump systems with time delay. J Franklin Inst 348:738–748

    Article  MathSciNet  MATH  Google Scholar 

  12. Xu ZB, Qiao H, Peng J, Zhang B (2004) A comparative study of two modeling approaches in neural networks. Neural Netw 17:73–85

    Article  MATH  Google Scholar 

  13. Li X, Song S (2014) Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method. Commun Nonlinear Sci Numer Simul 19:3892–3900

    Article  MathSciNet  Google Scholar 

  14. Li X, O’Regan Donal, Akca H (2015) Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays. IMA J Appl Math 80:85–99

    Article  MathSciNet  MATH  Google Scholar 

  15. 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 24:868–877

    Article  Google Scholar 

  16. Zuo Z, Yang C, Wang Y (2010) A new method for stability analysis recurrent neural networks with interval time-varying delay. IEEE Trans Neural Netw 21:339–344

    Article  Google Scholar 

  17. Bai YQ, Chen J (2013) New stability criteria for recurrent neural networks with interval time-varying delay. Neurocomputing 121:179–184

    Article  Google Scholar 

  18. Sun J, Chen J (2013) Stability analysis of static neural networks with interval time-varying delay. Appl Math Comput 221:111–120

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  20. Shao HY (2008) Delay-dependent stability for recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 19:1647–1651

    Article  Google Scholar 

  21. Zeng HB, He Y, Wu M, Zhang CF (2011) Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays. IEEE Trans Neural Netw 22:806–812

    Article  Google Scholar 

  22. Li T, Wang T, Song A, Fei S (2013) Combined convex technique on delay-dependent stability for delayed neural networks. IEEE Trans Neural Netw Learn Syst 24:1459–1466

    Article  Google Scholar 

  23. Ji MD, He Y, Zhang CK, Wu M (2014) Novel stability criteria for recurrent neural networks with time-varying delay. Neurocomputing 138:383–391

    Article  Google Scholar 

  24. Chen WH, Zheng WX (2008) Improved delay-dependent asymptotic stability criteria for delayed neural networks. IEEE Trans Neural Netw 19:2154–2161

    Article  Google Scholar 

  25. 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 25:1263–1276

    Article  Google Scholar 

  26. Kwon OM, Park Ju H, Lee SM, Cha EJ (2013) Analysis on delay-dependent stability for neural networks with time-varying delays. Neurocomputing 103:114–120

    Article  Google Scholar 

  27. Kwon OM, Lee SM, Park Ju H, Cha EJ (2012) New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput 218:9953–9964

    MathSciNet  MATH  Google Scholar 

  28. Zhou X, Tian J, Ma H, Zhong S (2014) Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays. Neurocomputing 129:401–408

    Article  Google Scholar 

  29. Ge C, Hua C, Ping X (2014) New delay-dependent stability criteria for neural networks with time-varying delay using delay-decomposition approach. IEEE Trans Neural Netw Learn Syst 25:1378–1383

    Article  Google Scholar 

  30. He Y, Liu G, Rees D, Wu M (2007) Stability analysis for neural networks with time-varying interval delay. IEEE Trans Neural Netw 18:1850–1854

    Article  Google Scholar 

  31. Tian J, Zhou X (2010) Improved asymptotic stability criteria for neural networks with interval time-varying delay. Expert Syst Appl 37:7521–7525

    Article  Google Scholar 

  32. Chen J, Sun J, Liu G, Rees D (2010) New delay-dependent stability criteria for neural networks with time-varying interval delay. Phys Lett A 374:4397–4405

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhang Y, Yue D, Tian E (2009) New stability criteria of neural networks with interval time-varying delays: a piecewise delay method. Appl Math Comput 208:249–259

    MathSciNet  MATH  Google Scholar 

  34. Wang J (2011) Novel delay-dependent stability criteria for neural networks with interval time-varying delay. Chin Phys B 20:120–701

    Google Scholar 

  35. Li T, Song A, Xue M, Zhang H (2011) Stability analysis on delayed neural networks based on an improved delay-partitioning approach. J Comput Appl Math 235:3086–3095

    Article  MathSciNet  MATH  Google Scholar 

  36. Wang Y, Yang C, Zuo Z (2012) On exponential stability analysis for neural networks with time-varying delays and general activation functions. Commun Nonlinear Sci Numer Simul 17:1447–1459

    Article  MathSciNet  MATH  Google Scholar 

  37. Kwon OM, Lee SM, Park Ju H, Cha EJ (2012) New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput 213:9953–9964

    MathSciNet  MATH  Google Scholar 

  38. Li X, Gao H, Yu X (2011) A unified approach to the stability of generalized static neural networks with linear fractional. IEEE Trans Syst Man Cybern B 41:1275–1286

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Zhang CK, He Y, Jiang L, Wu QH, Wu M (2013) Delay-dependent stability criteria for generalized neural networks with two delay components. IEEE Trans Neural Netw Learn Syst 25:1263–1276

    Article  Google Scholar 

  41. Raja R, Karthik Raja U, Samidurai R, Leelamani A (2014) Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays. Neural Comput Appl 25:751–766

    Article  MATH  Google Scholar 

  42. Samidurai R, Manivannan R (2015) Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components. Appl Math Comput 268:743–762

    MathSciNet  Google Scholar 

  43. Samidurai R, Manivannan R (2016) Delay-range-dependent passivity analysis for uncertain stochastic neural networks with discrete and distributed time-varying delays. Neurocomputing. doi:10.1016/j.neucom.2015.12.056

    Google Scholar 

  44. Samidurai R, Rajavel S, Zhu Q, Raja R, Zhou H (2016) Robust passivity analysis for neutral-type neural networks with mixed and leakage delays. Neurocomputing 175:635–643

    Article  Google Scholar 

  45. Kim SH, Park P, Jeong C (2010) Robust \(H_\infty\) stabilisation of networked control systems with packet analyser. IET Control Theory Appl 4:1828–1837

    Article  Google Scholar 

  46. Wang C, Shen Y (2012) Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time-varying delay. IET Control Theory Appl 6:875–883

    Article  MathSciNet  Google Scholar 

  47. Liu P (2015) New results on delay-range-dependent stability analysis for interval time-varying delay systems with non-linear perturbations. ISA Trans 57:93–100

    Article  Google Scholar 

  48. 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 23:467–479

    Article  MathSciNet  Google Scholar 

  49. 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 

  50. 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 

  51. 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 B 41:341–353

    Google Scholar 

  52. 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 

  53. Zhu Q, Cao J (2014) Mean-square exponential input-to-state stability of stochastic delayed neural networks. Neurocomputing 131:157–163

    Article  Google Scholar 

  54. Li N, Cao J (2013) Switched exponential state estimation and robust stability for interval neural networks with the average dwell time. IMA J Math Control Inf 32:257–276

    Article  MathSciNet  MATH  Google Scholar 

  55. Li N, Cao J, Hayat T (2014) Delay-decomposing approach to robust stability for switched interval networks with state-dependent switching. Cogn Neurodyn 8:313–326

    Article  Google Scholar 

  56. Cao J, Alofi A, Al-Mazrooei A, Elaiw A (2013) Synchronization of switched interval networks and applications to chaotic neural networks. Abstr Appl Anal 2013, Article ID 940573

  57. Cheng Q, Cao J (2011) Global synchronization of complex networks with discrete time delays and stochastic disturbances. Neural Comput Appl 20:1167–1179

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  60. Cao J (2000) Global asymptotic stability of neural networks with transmission delays. Int J Syst Sci 31:1313–1316

    Article  MATH  Google Scholar 

  61. Park MJ, Kwon OM, Park Ju H, Lee SM, Cha EJ (2015) Stability of time-delay systems via Wirtinger-based double integral inequality. Automatica 55:204–208

    Article  MathSciNet  Google Scholar 

  62. Gu K (2000) An integral inequality in the stability problem of time delay systems. In: Proceedings of the 39th IEEE conference on decision control, pp 2805–2810

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Acknowledgments

The authors would like to thank the Editor’s and anonymous Reviewer’s for their valuable suggestions and useful comments for the improvement of paper quality. Also, the work of first two authors would like to thank the Department of Science and Technology (DST), Government of India, New Delhi, for its financial support through the research project and Junior Research Fellowship (JRF).

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Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu, 632 115, India

    R. Manivannan, R. Samidurai & R. Sriraman

Authors
  1. R. Manivannan
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  2. R. Samidurai
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  3. R. Sriraman
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Corresponding author

Correspondence to R. Samidurai.

Additional information

This work was supported by Department of Science and Technology (DST), Government of India, New Delhi, under research project No. SR/FTP/MS-041/2011.

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Manivannan, R., Samidurai, R. & Sriraman, R. An improved delay-partitioning approach to stability criteria for generalized neural networks with interval time-varying delays. Neural Comput & Applic 28, 3353–3369 (2017). https://doi.org/10.1007/s00521-016-2220-0

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  • DOI: https://doi.org/10.1007/s00521-016-2220-0

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