Stability analysis of Markovian jumping impulsive stochastic delayed RDCGNNs with partially known transition probabilities

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• 作者：Weiyuan Zhang (1)
  
  1. Institute of Nonlinear Science ; Xianyang Normal University ; Xianyang ; Shaanxi ; 712000 ; P.R. China
  
• 关键词：impulsive ; stochastic reaction ; diffusion neural networks ; asymptotical stability ; Markovian jump ; mixed time delays
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：992 KB
• 参考文献：1. Zhang, H, Wang, Y (2008) Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 19: pp. 366-370 CrossRef
  2. Park, JH (2007) Further note on global exponential stability of uncertain cellular neural networks with variable delays. Appl. Math. Comput. 188: pp. 850-854 CrossRef
  3. Zhu, Q, Cao, J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 21: pp. 1314-1325 CrossRef
  4. Zhu, Q, Cao, J (2010) Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Neurocomputing 73: pp. 2671-2680 CrossRef
  5. Li, Z, Wen, C, Soh, Y (2001) Analysis and design of impulsive control systems. IEEE Trans. Autom. Control 46: pp. 894-897 CrossRef
  6. Xu, D, Yang, Z (2005) Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305: pp. 107-120 CrossRef
  7. Zhang, Y, Sun, J (2005) Stability of impulsive neural networks with time delays. Phys. Lett. A 348: pp. 44-50 CrossRef
  8. Song, Q, Zhang, J (2008) Global exponential stability of impulsive Cohen-Grossberg neural with time-varying delays. Nonlinear Anal., Real World Appl. 9: pp. 500-510 CrossRef
  9. Li, ZA, Li, KL (2009) Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms. Appl. Math. Model. 33: pp. 1337-1348 CrossRef
  10. Pan, J, Liu, X, Zhong, S (2010) Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. Math. Comput. Model. 51: pp. 1037-1050 CrossRef
  11. Li, K, Song, Q (2008) Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion term. Neurocomputing 72: pp. 231-240 CrossRef
  12. Wang, Z, Zhang, H (2010) Global asymptotic stability of reaction-diffusion Cohen-Grossberg neural network with continuously distributed delays. IEEE Trans. Neural Netw. 21: pp. 39-49 CrossRef
  13. Wang, Z, Zhang, H, Li, P (2010) An LMI approach to stability analysis of reaction-diffusion Cohen-Grossberg neural networks concerning Dirichlet boundary conditions and distributed delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40: pp. 1596-1606 CrossRef
  14. Vidhya, C, Balasubramaniam, P (2010) On the stability of the stochastic parabolic It么 equation with delay and Markovian jump. Comput. Math. Appl. 60: pp. 1959-1963 CrossRef
  15. Lv, Y, Lv, W, Sun, JH (2008) Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with continuously distributed delays. Nonlinear Anal., Real World Appl. 9: pp. 1590-1606 CrossRef
  16. Wan, L, Zhou, Q (2008) Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays. Appl. Math. Comput. 206: pp. 818-824 CrossRef
  17. Xu, X, Zhang, J, Zhang, W (2011) Mean square exponential stability of stochastic neural networks with reaction-diffusion terms and delay. Appl. Math. Lett. 24: pp. 5-11 CrossRef
  18. Wang, L, Xu, D (2003) Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays. Sci. China, Ser. F 46: pp. 466-474 CrossRef
  19. Wang, L, Zhang, Z, Wang, YF (2008) Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 372: pp. 3201-3209 CrossRef
  20. Teng, L, Yan, P (2011) Dynamical behaviors of reaction-diffusion fuzzy neural networks with mixed delays and general boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 16: pp. 993-1001 CrossRef
  21. Zhang, W, Li, J (2011) Global exponential stability of reaction-diffusion neural networks with discrete and distributed time-varying delays. Chin. Phys. B 20: CrossRef
  22. Zhu, Q, Li, X, Yang, X (2011) Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays. Appl. Math. Comput. 217: pp. 6078-6091 CrossRef
  23. Zhang, W, Li, J, Chen, M (2014) Pinning adaptive synchronization analysis of linearly coupled delayed RDNNs with unknown time-varying coupling strengths. Adv. Differ. Equ. 2014: CrossRef
  24. Zhang, W, Li, J, Chen, M (2013) Adaptive synchronization of the stochastic delayed RDNNs with unknown time-varying parameters. Adv. Differ. Equ. 2013: CrossRef
  25. Kao, Y-G, Guo, J-F, Wang, C-H, Sun, X-Q (2012) Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen-Grossberg neural networks with mixed delays. J. Franklin Inst. 349: pp. 1972-1988 CrossRef
  26. Rao, R, Zhong, S, Wang, X (2013) Delay-dependent exponential stability for Markovian jumping stochastic Cohen-Grossberg neural networks with p-Laplace diffusion and partially known transition rates via a differential inequality. Adv. Differ. Equ. 2013: CrossRef
  27. Zhang, L, Boukas, EK (2009) Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45: pp. 436-468 CrossRef
  28. Zhang, L, Boukas, EK, Lam, J (2009) Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Trans. Autom. Control 53: pp. 2458-2464 CrossRef
  29. Zhang, Y, He, Y, Wu, M, Zhang, J (2011) Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices. Automatica 47: pp. 79-84 CrossRef
  30. Lou, X, Cui, B (2009) Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters. Chaos Solitons Fractals 39: pp. 2188-2197 CrossRef
  31. Boyd, S, Ghaoui, L, Feron, E, Balakrishnan, V (1994) Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia CrossRef
  32. Mao, X (1997) Stochastic Differential Equations and Applications. Horwood, Chichester
  33. Gopalsamy, K, He, X (1994) Stability in asymmetric Hopfield nets with transmission delays. Physica D 76: pp. 344-358 CrossRef
  34. Stamova, IM, Ilarionov, R, Vaneva, R (2010) Impulsive control for a class of neural networks with bounded and unbounded delays. Appl. Math. Comput. 216: pp. 285-290 CrossRef
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

This paper considers the robust stability for a class of Markovian jump impulsive stochastic delayed reaction-diffusion Cohen-Grossberg neural networks with partially known transition probabilities. Based on the Lyapunov stability theory and linear matrix inequality (LMI) techniques, some robust stability conditions guaranteeing the global robust stability of the equilibrium point in the mean square sense are derived. To reduce the conservatism of the stability conditions, improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. An example shows the proposed theoretical result is feasible and effective.