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Robust stability analysis for uncertain recurrent neural networks with leakage delay based on delay-partitioning approach

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Abstract

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov–Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected.

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References

  1. Ong BT, Sugiura K, Zettsu K (2016) Dynamically pre-trained deep recurrent neural networks using environmental monitoring data for predicting PM2.5. Neural Comput Appl 27:1553–1566

    Article  Google Scholar 

  2. Li T, Zheng WX, Lin C (2011) Delay-slope-dependent stability results of recurrent neural networks. IEEE Trans Neural Netw 22:2138–2143

    Article  Google Scholar 

  3. Cao J, Wang J (2005) Exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans Circuits Syst I 52:920–931

    Article  MathSciNet  MATH  Google Scholar 

  4. Liu P (2013) Delay-dependent robust stability analysis for recurrent neural networks with time-varying delay. Int J Innov Comput Inf Control 9:3341–3355

    Google Scholar 

  5. Yang B, Wang R, Shi P, Dimirovski GM (2015) New delay-dependent stability criteria for recurrent neural networks with time-varying delays. Neurocomputing 151:1414–1422

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. 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 

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

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  10. Huang H, Feng G (2011) State estimation of recurrent neural networks with time-varying delay: a novel delay partition approach. Neurocomputing 74:792–796

    Article  Google Scholar 

  11. Wang ZS, Liu L, Shan QH, Zhang HG (2015) Stability criteria for recurrent neural networks with time-varying delay based on secondary partitioning method. IEEE Trans Neural Netw Learn Syst 26:2589–2595

    Article  MathSciNet  Google Scholar 

  12. Sakthivel R, Samidurai R, Anthoni SM (2010) Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects. J Optim Theory Appl 147:583–596

    Article  MathSciNet  MATH  Google Scholar 

  13. Ren F, Cao J (2008) Asymptotic and robust stability of genetic regulatory networks with time-varying delays. Neurocomputing 71:834–842

    Article  Google Scholar 

  14. Mathiyalagan K, Su H, Shi P, Sakthivel R (2015) Exponential \({\fancyscript {H}}_{\infty }\) filtering for discrete-time switched neural networks with random delays. IEEE Trans Cybern 45:676–687

    Article  Google Scholar 

  15. Mathiyalagan K, Sakthivel R, Anthoni SM (2012) Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks. Phys Lett A 376:901–912

    Article  MATH  Google Scholar 

  16. Mathiyalagan K, Sakthivel R, Anthoni SM (2011) New stability and stabilization criteria for fuzzy neural networks with various activation functions. Phys Scripta 84. Article ID 015007

  17. Mathiyalagan K, Sakthivel R, Anthoni SM (2012) New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays. Commun Nonlinear Sci 17:1392–1407

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang XM, Han QL (2009) A delay decomposition to delay-dependent stability for linear systems with time-varying delays. Int J Robust Nonlinear 19:1922–1930

    Article  MathSciNet  MATH  Google Scholar 

  19. Manivannan R, Samidurai R, Sriraman R (2016) An improved delay-partitioning approach to stability criteria for generalized neural networks with interval time-varying delays. Neural Comput Appl. doi:10.1007/s00521-016-2220-0

    Google Scholar 

  20. Sun J, Liu G, Chen J, Rees D (2009) Improved stability criteria for neural networks with time-varying delay. Phys Lett A 373:342–348

    Article  MATH  Google Scholar 

  21. 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 

  22. Ji MD, He Y, Wu M, Zhang CK (2015) Further results on exponential stability of neural networks with time-varying delay. Appl Math Comput 256:175–182

    MathSciNet  MATH  Google Scholar 

  23. Gopalsamy P (2007) Leakage delays in BAM. J Math Appl 325:1117–1132

    MathSciNet  MATH  Google Scholar 

  24. Wang H, Li C, Xu H (2009) Existence and global exponential stability of periodic solution of cellular neural networks with impulses and leakage delay. Int J Bifur Chaos 19:831–842

    Article  MathSciNet  MATH  Google Scholar 

  25. Sakthivel R, Vadivel P, Mathiyalagan K, Arunkumar A, Sivachitra M (2015) Design of state estimator bidirectional associative memory neural network with leakage delays. Inf Sci 296:263–274

    Article  MathSciNet  MATH  Google Scholar 

  26. 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 

  27. 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 

  28. Chen Z, Liu B (2013) Convergence behavior of Cohen-Grossberg neural networks with time-varying delays in the leakage terms. Neurocomputing 120:518–523

    Article  Google Scholar 

  29. Peng S (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal RWA 11:2141–2151

    Article  MathSciNet  MATH  Google Scholar 

  30. Li Y, Yang L, Sun LJ (2013) Existence and exponential stability of an equilibrium point for fuzzy BAM neural networks with time-varying delays in leakage terms on time scales. Adv Differ Equ 2013:218. doi:10.1186/1687-1847-2013-218

    Article  MathSciNet  MATH  Google Scholar 

  31. Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Global asymptotic stability of BAM fuzzy cellular neural networks with time delays in the leakage term, discrete and unbounded distributed delays. Math Comput Model 53:839–853

    Article  MathSciNet  MATH  Google Scholar 

  32. Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal RWA 14:559–566

    Article  MathSciNet  MATH  Google Scholar 

  33. Li X, Cao J (2010) Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 23:1709–1726

    Article  MathSciNet  MATH  Google Scholar 

  34. Chen XF, Song QK (2013) Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales. Neurocomputing 121:254–264

    Article  Google Scholar 

  35. Tian JK, Zhong SM (2011) Improved delay-dependent stability criterion for neural networks with time-varying delay. Appl Math Comput 217:10278–10288

    MathSciNet  MATH  Google Scholar 

  36. Park P, Ko J, Jeong C (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47:235–238

    Article  MathSciNet  MATH  Google Scholar 

  37. He Y, Ji MD, Zhang CK, Wu M (2016) Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality. Neural Netw 77:80–86

    Article  Google Scholar 

  38. He Y, Liu G, Rees D (2007) New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans Neural Netw 18:310–314

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  41. Wu L, Feng Z, Zheng W (2010) Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE Trans Neural Netw 21:1396–1407

    Article  Google Scholar 

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

    Article  Google Scholar 

  43. Zhu XL, Yang GH (2008) New delay-dependent stability results for neural networks with time-varying delay. IEEE Trans Neural Netw 19(10):1783–1791

    Article  Google Scholar 

  44. Kwon OM, Park MJ, Park JH, Lee SM, Cha EJ (2014) On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov–Krasovskii functional. Commun Nonlinear Sci Numer Simul 19:3184–3201

    Article  MathSciNet  MATH  Google Scholar 

  45. Kwon OM, Lee SM, Park JH, 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 

Download references

Acknowledgements

The authors are very thankful to the editor and reviewers for their useful comments and helpful suggestions. This work is partly supported by NSFC under Grant Nos. 61271355 and 61375063, the ZNDXYJSJGXM under Grant No. 2015J-GB21 and the Educational Department of Hunan Province of China under Grant No. 15C0243.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China

    Sai-Bing Qiu, Xin-Ge Liu, Feng-Xian Wang & Yan-Jun Shu

  2. College of Mathematics and Computer Science, Hunan City University, Yiyang, 413000, Hunan, China

    Sai-Bing Qiu

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  1. Sai-Bing Qiu
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Correspondence to Xin-Ge Liu.

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Qiu, SB., Liu, XG., Wang, FX. et al. Robust stability analysis for uncertain recurrent neural networks with leakage delay based on delay-partitioning approach. Neural Comput & Applic 30, 211–222 (2018). https://doi.org/10.1007/s00521-016-2670-4

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  • DOI: https://doi.org/10.1007/s00521-016-2670-4

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