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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 212469, 11 pages
http://dx.doi.org/10.1155/2013/212469
Research Article

Stability Analysis of Stochastic Markovian Jump Neural Networks with Different Time Scales and Randomly Occurred Nonlinearities Based on Delay-Partitioning Projection Approach

1School of Science, Jiangnan University, Wuxi 214122, China
2Key Laboratory of Advanced Process Control for Light Industry (Jiangnan University), Ministry of Education, Wuxi 214122, China

Received 27 June 2013; Accepted 2 October 2013

Academic Editor: Debora Amadori

Copyright © 2013 Jianmin Duan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Arik, “Global asymptotic stability of a class of dynamical neural networks,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 4, pp. 568–571, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  2. X. S. Yang, J. D. Cao, and J. Q. Lu, “Synchronization of delayed complex dynamical networks with impulsive and stochastic effects,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2252–2266, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. D. Cao, G. R. Chen, and P. Li, “Global synchronization in an array of delayed neural networks with hybrid coupling,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 38, no. 2, pp. 488–498, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. J. D. Cao, Z. D. Wang, and Y. H. Sun, “Synchronization in an array of linearly stochastically coupled networks with time delays,” Physica A, vol. 385, no. 2, pp. 718–728, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  5. Z. Orman and S. Arik, “An analysis of stability of a class of neutral-type neural networks with discrete time delays,” Abstract and Applied Analysis, vol. 2013, Article ID 143585, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Q. Luo, X. J. Miao, Q. Wei, and Z. X. Zhou, “Stability of impulsive neural networks with time-varying and distributed delays,” Abstract and Applied Analysis, vol. 2013, Article ID 325310, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. X. Y. Meng, J. Lam, B. Z. Du, and H. J. Gao, “A delay-partitioning approach to the stability analysis of discrete-time systems,” Automatica, vol. 46, no. 3, pp. 610–614, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  8. O. M. Kwon, M. J. Park, J. H. Park, S. M. Lee, and E. J. Cha, “Improved criteria on delay-dependent stability for discrete-time neural networks with interval time-varying delays,” Abstract and Applied Analysis, vol. 2012, Article ID 285931, 16 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. Du, J. Lam, Z. Shu, and Z. Wang, “A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components,” IET Control Theory and Applications, vol. 3, no. 4, pp. 383–390, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. H. B. Zeng, Y. He, M. Wu, and C. Zhang, “Complete delay-decomposing approach to asymptotic stability for neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 22, no. 5, pp. 806–812, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. B. Z. Du and J. Lam, “Stability analysis of static recurrent neural networks using delay-partitioning and projection,” Neural Networks, vol. 22, no. 4, pp. 343–347, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. W. M. Chen, Q. Ma, G. Y. Miao, and Y. J. Zhang, “Stability analysis of stochastic neural networks with Markovian jump parameters using delaypartitioning approach,” Neurocomputing, vol. 103, pp. 22–28, 2013. View at Publisher · View at Google Scholar
  13. L. Wan and J. H. Sun, “Mean square exponential stability of stochastic delayed Hopfield neural networks,” Physics Letters A, vol. 343, no. 4, pp. 306–318, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Y. Shao and Q. L. Han, “New stability criteria for linear discrete-time systems with interval-like time-varying delays,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 619–625, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. Arik, “Stability analysis of delayed neural networks,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 7, pp. 1089–1092, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Y. Chen and W. X. Zheng, “Stochastic state estimation for neural networks with distributed delays and Markovian jump,” Neural Networks, vol. 25, pp. 14–20, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. S. P. Wen, Z. G. Zeng, and T. W. Huang, “Reliable H filter design for a class of mixed-delay Markovian jump systems with stochastic nonlinearities and multiplicative noises via delay-partitiong method,” International Journal of Control, Automation and Systems, vol. 10, no. 4, pp. 711–720, 2012. View at Publisher · View at Google Scholar
  18. Y. Kang, W. K. Shang, and H. S. Xi, “Estimating the delay-time for the stability of Markovian jump bilinear systems with saturating actuators,” Acta Automatica Sinica, vol. 36, no. 5, pp. 762–767, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L. L. Xiong, J. K. Tian, and X. Z. Liu, “Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities,” Journal of the Franklin Institute, vol. 349, no. 6, pp. 2193–2214, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. Q. X. Zhu and J. D. Cao, “Stability of Markovian jump neural networks with impulse control and time varying delays,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2259–2270, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. Q. Ma, S. Y. Xu, Y. Zou, and J. J. Lu, “Stability of stochastic Markovian jump neural networks with mode-dependent delays,” Neurocomputing, vol. 74, no. 12-13, pp. 2157–2163, 2011. View at Publisher · View at Google Scholar · View at Scopus
  22. Q. X. Zhu and J. D. Cao, “Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 3, pp. 467–479, 2010. View at Publisher · View at Google Scholar
  23. H. Y. Li, Q. Zhou, B. Chen, and H. H. Liu, “Parameter-dependent robust stability for uncertain Markovian jump systems with time delay,” Journal of the Franklin Institute, vol. 348, no. 4, pp. 738–748, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  24. Y. F. Guo and Z. J. Wang, “Stability of Markovian jump systems with generally uncertain transition rates,” Nonlinear Dynamics, vol. 350, pp. 2826–2836, 2013.
  25. Z. D. Wang, Y. Wang, and Y. R. Liu, “Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 11–25, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. S. Liu, Z. D. Wang, and W. Wang, “Reliable H filtering for discrete time-delay systems with randomly occurred nonlinearities via delay-partitioning method,” Signal Processing, vol. 91, no. 4, pp. 713–727, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley-Interscience, London, UK, 1974. View at MathSciNet
  28. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, Amsterdam, The Netherlands, 2006.
  29. C. Wang and Y. Shen, “Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time-varying delay,” IET Control Theory and Applications, vol. 6, no. 7, pp. 875–883, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  30. J. Yu, K. Zhang, and S. Fei, “Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 207–216, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  31. Y. He, J. H. She, and M. Wu, “New delay-dependent stability criteria and stabilizing method for neutral systems,” IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2266–2271, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  32. C. G. Li, L. N. Chen, and K. Aihara, “Stability of genetic networks with SUM regulatory logic: Lur'e system and LMI approach,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 11, pp. 2451–2458, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  33. H. Huang and G. Feng, “State estimation of recurrent neural networks with time-varying delay: a novel delay partition approach,” Neurocomputing, vol. 74, no. 5, pp. 792–796, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. G. F. Song and Z. Wang, “A delay partitioning approach to output feedback control for uncertain discrete time-delay systems with actuator saturation,” Nonlinear Dynamics, vol. 74, no. 1-2, pp. 189–202, 2013. View at Publisher · View at Google Scholar
  35. Q. T. Gan, “Synchronization of competitive neural networks with diffetent time scales and time-varying delay based on delay partitioning approach,” International Journal of Machine Learning and Cybernetics, vol. 4, no. 4, pp. 327–337, 2013. View at Publisher · View at Google Scholar
  36. Q. X. Cheng and J. D. Cao, “Global synchronization of complex networks with discrete time delays on time scales,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 287670, 19 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  37. Y. P. Ren and Y. K. Li, “Stability and existence of periodic solutions for cellular neural networks with state dependent delays on time scales,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 386706, 14 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  38. Y. Zhao, H. J. Gao, J. Lam, and B. Z. Du, “Stability and stabilization of delayed T-S fuzzy systems: a delay partitioning approach,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 4, pp. 750–762, 2009. View at Publisher · View at Google Scholar · View at Scopus
  39. J. Lam, H. J. Gao, and C. H. Wang, “Stability analysis for continuous systems with two additive time-varying delay components,” Systems and Control Letters, vol. 56, no. 1, pp. 16–24, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  40. Q. L. Han and K. Q. Gu, “Stability of linear systems with time-varying delay: a generalized discretized lyapunov functional approach,” Asian Journal of Control, vol. 3, no. 3, pp. 170–180, 2001. View at Scopus
  41. Q. S. Liu, J. Wang, and J. D. Cao, “A delayed lagrangian network for solving quadratic programming problems with equality constraints,” in Advances in Neural Networks—ISNN 2006, vol. 3971 of Lecture Notes in Computer Science, pp. 369–378, Springer, New York, NY, USA, 2006. View at Scopus
  42. H. Y. Liu, L. Zhao, Z. X. Zhang, and Y. Ou, “Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays,” Neurocomputing, vol. 72, no. 16–18, pp. 3669–3674, 2009. View at Publisher · View at Google Scholar · View at Scopus
  43. J. M. Duan, M. F. Hu, Y. Q. Yang, and L. X. Liu, “A delay partitioning projection approach to stability analysis of stochastic Markovian jump neural networks with randomly occurred nonlinearities,” Neurocomputing. In press.
  44. J. M. Duan, M. F. Hu, and Y. Q. Yang, “A delay-partitioning approach to stability analysis of discrete-time recurrent neural networks with randomly occurred nonlinearities,” in Advances in Neural Networks—ISNN 2013, vol. 7951, pp. 197–204, Springer, New York, NY, USA, 2013. View at Publisher · View at Google Scholar
  45. Y. Q. Xia, M. Y. Fu, and P. Shi, Analysis and Synthesis of Dynamical Systems with Time-Delays, vol. 387 of Lecture Notes in Control and Information Sciences, Springer, New York, NY, USA, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  46. C. Peng and Y. C. Tian, “Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay,” IET Control Theory and Applications, vol. 2, no. 9, pp. 752–761, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  47. S. Lakshmanan, J. H. Park, H. Y. Jung, O. M. Kwon, and R. Rakkiyappan, “A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays,” Neurocomputing, vol. 111, pp. 81–89, 2013. View at Publisher · View at Google Scholar