Global exponential estimates of delayed stochastic neural networks with Markovian switching

Neural Networks

Volumn 36, Issue , 2012, Pages 136-145

  Huang, He ^a   Huang, Tingwen ^b   Chen, Xiaoping ^a  

^a SOOCHOW UNIVERSITY   (China)

^b TEXAS A AND M UNIVERSITY AT QATAR   (Qatar)

Author keywords

Exponential estimates; Markovian switching; Mode dependent; Stochastic neural networks; Time delay

Indexed keywords

DECAY RATE; EXPONENTIAL ESTIMATES; EXPONENTIALLY STABLE; INHERENT CHARACTERISTICS; LYAPUNOV FUNCTIONALS; MARKOVIAN SWITCHING; MEAN SQUARE; MODE-DEPENDENT; NUMERICAL EXAMPLE; PARAMETER UNCERTAINTY; POSITIVE-DEFINITE MATRICES; STABILITY CONDITION; STOCHASTIC NEURAL NETWORK; SYSTEM MODE; TIME-VARYING DELAY;

DECAY (ORGANIC); LYAPUNOV FUNCTIONS; TIME DELAY;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; GLOBAL EXPONENTIAL ESTIMATION; MARKOVIAN SWITCHING; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; PROBABILITY; STATISTICAL ANALYSIS; STATISTICAL PARAMETERS; STOCHASTIC MODEL; TIME; UNCERTAINTY;

ALGORITHMS; COMPUTER SIMULATION; MARKOV CHAINS; NEURAL NETWORKS (COMPUTER); STOCHASTIC PROCESSES; TIME FACTORS;

EID: 84868254478     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2012.10.002     Document Type: Article

References (40)

1. Ariba, Y., & Gouaisbaut, F. (2007). Delay-dependent stability analysis of linear systems with time-varying delay. In Proc. of the 46th IEEE conf. on decision and control (pp. 2053-2058). New Orleans, LA, UAS.
2. Balasubramaniam P., Lakshmanan S. Delay-range dependent stability criteria for neural networks with Markovian jumping parameters. Nonlinear Analysis: Hybrid Systems 2009, 3:749-756.
3. Blythe S., Mao X., Shah A. Razumikhin-type theorems on stability of stochastic neural networks with delays. Stochastic Analysis and Applications 2001, 19:85-101.
4. Boyd S., El Ghaoui L., Feron E., Balakrishnan V. Linear matrix inequalities in system and control theory 1994, SIAM, Philadelphia, PA.
5. Chen W., Zheng W.X. Robust stability analysis for stochastic neural networks with time-varying delay. IEEE Transactions on Neural Networks 2010, 21(3):508-514.
6. Faydasicok O., Arik S. Robust stability analysis of a class of neural networks with discrete time delays. Neural Networks 2012, 29-30:52-59.
7. Haykin S. Neural networks: a comprehensive foundation 1999, Prentice-Hall, Upper Saddle River, NJ. 2nd ed.
8. Huang H., Ho D.W.C., Qu Y. Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Networks 2007, 20:799-809.
9. Liao X., Mao X. Exponential stability and instability of stochastic neural networks. Stochastic Analysis and Applications 1996, 14:165-185.
10. Li X., Gao H., Yu X. A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2011, 41(5):1275-1286.
11. Liu X., Chen T., Cao J., Lu W. Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches. Neural Networks 2011, 24:1013-1021.
12. Liu H., Ou Y., Hu J., Liu T. Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters. Neural Networks 2010, 23:315-321.
13. Liu Y., Wang Z., Liang J., Liu X. Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Transactions on Neural Networks 2009, 20(7):1102-1116.
14. Liu Y., Wang Z., Liu X. On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching. Nonlinear Dynamics 2008, 54:199-212.
15. Lou X., Cui B. Stochastic exponential stability for Markovian jumping BAM neural networks with time-varying delays. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2007, 37(3):713-719.
16. Ma Q., Xu S., Zou Y., Lu J. Stability of stochastic Markovian jump neural networks with mode-dependent delays. Neurocomputing 2011, 74:2157-2163.
17. Mao X. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Transactions on Automatic Control 2002, 47(10):1604-1612.
18. Mao X., Matasov A., Piunovskiy A.B. Stochastic differential delay equations with Markovian switching. Bernoulli 2000, 6(1):73-90.
19. Marco M.D., Grazzini M., Pancioni L. Global robust stability criteria for interval delayed full-range cellular neural networks. IEEE Transactions on Neural Networks 2011, 22(4):666-671.
20. Roska T., Chua L.O. Cellular neural networks with nonlinear and delay-type template. International Journal of Circuit Theory and Applications 1992, 20:469-481.
21. Shen Y., Wang J. Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters. IEEE Transactions on Neural Networks 2007, 18(6):1857-1862.
22. Shu Z., Lam J. Global exponential estimates of stochastic interval neural networks with discrete and distributed delays. Neurocomputing 2008, 71:2950-2963.
23. Skorohod A.V. Asymptotic methods in the theory of stochastic differential equations 1989, Amer. Math. Soc., Providence, RI.
24. Tino P., Cernansky M., Benuskova L. Markovian architectural bias of recurrent neural networks. IEEE Transactions on Neural Networks 2004, 15(1):6-15.
25. Wang Z., Liu Y., Li M., Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2006, 17:814-820.
26. Wang Z., Liu Y., Yu L., Liu X. Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Physics Letters A 2006, 356:346-352.
27. Wu M., Liu F., Shi P., He Y., Yokoyama R. Exponential stability analysis for neural networks with time-varying delay. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2008, 38(4):1152-1156.
28. Wu Z., Shi P., Su H., Chu J. Delay-dependent stability analysis for switched neural networks with time-varying delay. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2011, 41(6):1522-1530.
29. Wu Z., Shi P., Su H., Chu J. Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays. Expert Systems with Applications 2012, 39:6174-6181.
30. ∞ control and quadratic stabilization of systems with uncertainty via output feedback. IEEE Transactions on Automatic Control 1992, 37(8):1253-1256.
31. Yang X., Cao J., Lu J. Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Transactions on Neural Networks and Learning Systems 2012, 23(1):60-71.
32. Yang R., Gao H., Shi P. Novel robust stability criteria for stochastic Hopfield neural networks. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2009, 39(2):467-474.
33. Zeng Z., Wang J. Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli. Neural Networks 2006, 19:1528-1537.
34. Zhang X., Han Q. New Lyapunov-Krasovskii functionals for global asymptotical stability of delayed neural networks. IEEE Transactions on Neural Networks 2009, 20(3):533-539.
35. Zhang H., Liu Z., Huang G., Wang Z. Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Transactions on Neural Networks 2010, 21(1):91-106.
36. Zhang H., Wang Y. Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2008, 19(2):366-370.
37. Zhang B., Xu S., Zong G., Zou Y. Delay-dependent exponential stability for uncertain stochastic Hopfield neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I: Regular Papers 2009, 56(6):1241-1247.
38. Zheng C., Zhang H., Wang Z. Novel exponential stability criteria of high-order neural networks with time-varying delays. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2011, 41(2):486-496.
39. Zhu Q., Cao J. Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks 2010, 21(8):1314-1325.
40. Zhu Q., Cao J. Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 2011, 41(2):341-353.