Robust Stability of Markovian Jump Stochastic Neural Networks with Time Delays in the Leakage Terms

详细信息    查看全文

• 作者：Quanxin Zhu (1)
  Jinde Cao (2) (4)
  Tasawar Hayat (3) (4)
  Fuad Alsaadi (5)
  
  1. School of Mathematical Sciences and Institute of Finance and Statistics ; Nanjing Normal University ; Nanjing聽 ; 210023 ; Jiangsu ; China
  2. Department of Mathematics and Research Center for Complex Systems and Network Sciences ; Southeast University ; Nanjing聽 ; 210096 ; Jiangsu ; China
  4. Department of Mathematics ; Faculty of Science ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  3. Department of Mathematics ; Quaid-I-Azam University ; Islamabad聽 ; 44000 ; Pakistan
  5. Department of Electrical and Computer Engineering ; Faculty of Engineering ; King Abdulaziz University ; Jeddah ; Saudi Arabia
  
• 关键词：Exponential stability ; Stochastic neural network ; Lyapunov functional ; Linear matrix inequality ; Markovian jump parameter ; Leakage time delay
• 刊名：Neural Processing Letters
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：41
• 期：1
• 页码：1-27
• 全文大小：425 KB
• 参考文献：1. Arik S (2000) Stability analysis of delayed neural networks. IEEE Trans Circuits Syst I 47(7):1089鈥?1092 CrossRef
  2. Arik S, Orman Z (2005) Global stability analysis of Cohen鈥揋rossberg neural networks with time varying delays. Phys Lett A 341(5鈥?):410鈥?21 CrossRef
  3. Joy MP (2000) Results concerning the absolute stability of delayed neural networks. Neural Netw 13(6):613鈥?16 CrossRef
  4. Blythe S, Mao X, Liao X (2001) Stability of stochastic delay neural networks. J Frankl Inst 338(4):481鈥?95 CrossRef
  5. Arik S, Tavsanoglu V (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays. Neurocomputing 68:161鈥?76 CrossRef
  6. Huang H, Ho DWC, Lam J (2005) Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans Circuits Syst II 52(5):251鈥?55 CrossRef
  7. Javidmanesh E, Afsharnezhad Z, Effati S (2013) Existence and stability analysis of bifurcating periodic solutions in a delayed five-neuron BAM neural network model. Nonlinear Dyn 72:149鈥?64 CrossRef
  8. Rakkiyappan R, Balasubramaniam P (2008) Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl Math Comput 198(2):526鈥?33 CrossRef
  9. Zhou Q, Wan L (2008) Exponential stability of stochastic delayed Hopfield neural networks. Appl Math Comput 199(1):84鈥?9 CrossRef
  10. Xu S, Lam J (2006) A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Netw 19(1):76鈥?3 CrossRef
  11. Moon YS, Park P, Kwon WH, Lee YS (2001) Delay-dependent robust stabilization of uncertain state-delayed systems. Int J Control 74(14):1447鈥?455 CrossRef
  12. Chen Y (2002) Global stability of neural networks with distributed delays. Neural Netw 15(7):867鈥?71 CrossRef
  13. Chen W, Zheng W (2007) Delay-dependent robust stabilization for uncertain neutral systems with distributed delays. Automatica 43(1):95鈥?04 CrossRef
  14. Park JH (2008) On global stability criterion of neural networks with continuously distributed delays. Chaos Solitons Fractals 37(2):444鈥?49 CrossRef
  15. Zhao H (2004) Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Netw 17(1):47鈥?3 CrossRef
  16. Yang H, Chu T (2007) LMI conditions for stability of neural networks with distributed delays. Chaos Solitons Fractals 34(2):557鈥?63 CrossRef
  17. Liu X, Wang Z, Liu X (2006) On global exponential stability of generalized stochastic neural networks with mixed time delays. Neurocomputing 70(1鈥?):314鈥?26 CrossRef
  18. Wang Z, Liu Y, Liu X (2005) On global asymptotic stability of neural networks with discrete and distributed delays. Phys Lett A 345(4鈥?):299鈥?08 CrossRef
  19. Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325(2):1117鈥?132 CrossRef
  20. Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math Comput Model 53(5鈥?):839鈥?53 CrossRef
  21. Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst Signal Process 30(6):1595鈥?616 CrossRef
  22. Li X, Fu X, Balasubramaniam P, Rakkiyappan R (2010) Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations. Nonlinear Anal RWA 11(5):4092C4108
  23. Li X, Rakkiyappan R, Balasubramaniam P (2011) Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Frankl Inst 348(2):135鈥?55 CrossRef
  24. Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal RWA 14(1):559鈥?66 CrossRef
  25. Long S, Song Q, Wang X, Li D (2012) Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations. J Frankl Inst 349(7):2461鈥?479 CrossRef
  26. 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(1):365鈥?78 CrossRef
  27. Lakshmanan S, Park JH, Lee TH, Jung HY, Rakkiyappan R (2013) Stability criteria for BAM neural networks with leakage delays and probabilistic time-varying delays. Appl Math Comput 219(17):9408鈥?423 CrossRef
  28. Lakshmanan S, Park JH, Jung HY (2013) Robust delay-dependent stability criteria for dynamic systems with nonlinear perturbations and leakage delay. Circuits Syst Signal Process 32(4):1637鈥?657 CrossRef
  29. Balasubramaniam P, Vembarasan V, Rakkiyappan R (2012) Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term. Neural Comput Appl 21(7):1593鈥?616 CrossRef
  30. Balasubramaniam P, Vembarasan V, Rakkiyappan R (2011) Leakage delays in T鈥揝 fuzzy cellular neural networks. Neural Process Lett 33(2):111鈥?36 CrossRef
  31. Balasubramaniam P, Vembarasan V (2011) Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term. Int J Comput Math 88(15):3271鈥?291 CrossRef
  32. Liu Y, Wang Z, Liu X (2008) On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching. Nonlinear Dyn 54(3):199鈥?12 CrossRef
  33. Balasubramaniam P, Vembarasan V (2011) Robust stability of uncertain fuzzy BAM neural networks of neutral-type with Markovian jumping parameters and impulses. Comput Math Appl 62(4):1838鈥?861 CrossRef
  34. Balasubramaniam P, Vembarasan V, Rakkiyappan R (2011) Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. Commun Nonlinear Sci Numer Simul 16(4):2109鈥?129 CrossRef
  35. Balasubramaniam P, Rakkiyappan R (2009) Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen鈥揋rossberg neural networks with discrete interval and distributed time-varying delays. Nonlinear Anal Hybrid Syst 3(3):207鈥?14 CrossRef
  36. Zhang H, Wang Y (2008) Stability analysis of Markovian jumping stochastic Cohen鈥揋rossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19(2):366鈥?70 CrossRef
  37. 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(2):341鈥?53
  38. Zhu Q, Cao J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen鈥揋rossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21(8):1314鈥?325 CrossRef
  39. 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鈥?79 CrossRef
  40. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference on decision and control, Sydney, pp 2805鈥?810
  41. Wang Z, Liu Y, Yu L, Liu X (2006) Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356(4鈥?):346鈥?52 CrossRef
  42. Zhang Y (2013) Stochastic stability of discrete-time Markovian jump delay neural networks with impulses and incomplete information on transition probability. Neural Netw 46:276鈥?82 CrossRef
  43. Zhu S, Shen Y (2013) Robustness analysis for connection weight matrices of global exponential stability of stochastic recurrent neural networks. Neural Netw 38:17鈥?2 CrossRef
  44. Faydasicok O, Arik S (2012) Robust stability analysis of a class of neural networks with discrete time delays. Neural Netw 29鈥?0:52鈥?9 CrossRef
  45. Zhou T, Wang M, Long M (2012) Existence and exponential stability of multiple periodic solutions for a multidirectional associative memory neural network. Neural Process Lett 35(2):187鈥?02 CrossRef
  46. Zheng C, Shan Q, Wang Z (2012) Improved stability results for stochastic Cohen鈥揋rossberg neural networks with discrete and distributed delays. Neural Process Lett 35(2):103鈥?29 CrossRef
  47. Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia CrossRef
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Complexity
  Artificial Intelligence and Robotics
  Electronic and Computer Engineering
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-773X

文摘

This paper deals with the problem of exponential stability for a class of Markovian jump stochastic neural networks with time delays in the leakage terms and mixed time delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain, and the mixed time delays consist of time-varying delays and distributed delays. By using the method of model transformation, Lyapunov stability theory, stochastic analysis and linear matrix inequalities techniques, several novel sufficient conditions are derived to guarantee the exponential stability in the mean square of the equilibrium point of the suggested system in two cases: with known or unknown parameters. Moreover, some remarks and discussions are given to illustrate that the obtained results are significant, which comprises and generalizes those obtained in the previous literature. In particular, the obtained stability conditions are delay-dependent, which depends on all the delay constants, and thus the presented results are less conservatism. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.