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Su, Weiwei; Chen, Yiming

Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays. (English) Zbl 1221.37196

Commun. Nonlinear Sci. Numer. Simul. 14, No. 2, 520-528 (2009).
Summary: The paper is concerned with the problem of robust asymptotic stability analysis of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technology, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed conditions can be checked easily with the LMI Control Toolbox in Matlab. Furthermore, all the results are obtained under mild conditions, assuming neither differentiability nor strict monotonicity for activation function. A numerical example is given to demonstrate the effectiveness of our results.

Cited in 27 Documents

MSC:

37N25 Dynamical systems in biology
34K20 Stability theory of functional-differential equations
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
62M45 Neural nets and related approaches to inference from stochastic processes
92B20 Neural networks for/in biological studies, artificial life and related topics

Keywords:

stochastic Cohen-Grossberg neural networks; delay-dependent robust stability; discrete and distributed time-varying delays; norm-bounded uncertainties

Software:

Matlab
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\textit{W. Su} and \textit{Y. Chen}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 2, 520--528 (2009; Zbl 1221.37196)
Full Text: DOI

References:

[2] Singh, V., New global robust stability results for delayed cellular neural networks based on norm-bounded uncertainties, Chaos Soliton Fract, 30, 1165-1171 (2006) · Zbl 1142.34353
[3] Park, Ju H., A novel criterion for global asymptotic stability of BAM neural networks with time delays, Chaos Soliton Fract, 29, 446-453 (2006) · Zbl 1121.92006
[4] Cohen, M. A.; Grossberg, S., Absolute stability and global pattern formulation and parallel memory storage by competitive neural networks, IEEE Trans Syst Man Cybernetics, SMC-13, 815-821 (1983) · Zbl 0553.92009
[5] Chen, T. P.; Rong, L. B., Robust global exponential stability of Cohen-Grossberg neural networks with time delays, IEEE Trans Neural Networks, 15, 1, 203-206 (2004)
[6] Liao, X.; Li, C.; Wong, K. W., Criteria for exponential stability of Cohen-Grossberg neural networks, Neural Networks, 17, 1401-1414 (2004) · Zbl 1073.68073
[7] Wang, L.; Zou, X., Exponential stability of Cohen-Grossberg neural networks, Neural Networks, 15, 415-422 (2002)
[8] Jiang, H. J.; Cao, J. D.; Teng, Z. D., Dynamics of Cohen-Grossberg neural networks with time-varying delays, Phys Lett A, 354, 414-422 (2006)
[9] Zhao, W. R.; Tan, Y., Harmless delays for global exponential stability of Cohen-Grossberg neural networks, Math Comput Simulat, 74, 47-57 (2007) · Zbl 1119.34055
[12] Rong, L. B., LMI-based criteria for robust stability of Cohen-Grossberg neural networks with delay, Phys Lett A, 339, 63-73 (2005) · Zbl 1137.93401
[14] Cao, J. D.; Li, X. L., Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach, Physica D, 212, 54-65 (2005) · Zbl 1097.34053
[15] Zhou, L.; Zhou, M. R., Stability analysis of a class of generalized neural networks with delays, Phys Lett A, 337, 203-215 (2005) · Zbl 1135.34339
[16] Arik, S.; Orman, Z., Global stability analysis of Gohen-Grossberg neural metworks with time varying delays, Phys Lett A, 341, 410-421 (2005) · Zbl 1171.37337
[17] Lu, W.; Chen, T., New condition on global stability of Cohen-Grossberg neural networks, Neural Comput, 15, 1173-1189 (2006) · Zbl 1086.68573
[18] Liu, J., Global exponential stabilities of Cohen-Grossberg neural networks with time-varying delays, Chaos Soliton fract, 26, 935-945 (2005) · Zbl 1138.34349
[19] Wan, L.; Sun, J. H., Global asymptotic stability of Cohen-Grossberg neural networks with continuously distributed delays, Phys Lett A, 342, 331-340 (2005) · Zbl 1222.93200
[21] Zhang, J. H.; Shi, P.; Qiu, J. Q., Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear Anal: Real World Appl, 8, 1349-1357 (2007) · Zbl 1124.34056
[22] Wang, Z. D.; Liu, Y. R.; Fraser, K.; Liu, X. H., Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays, Phys Lett A, 354, 288-297 (2006) · Zbl 1181.93068
[23] Zhao, H. Y.; Ding, N., Dynamic analysis of stochastic Cohen-Grossberg neural networks with time delays, Appl Math Comput, 183, 464-470 (2006) · Zbl 1117.34080
[24] Wang, Z. D.; Liu, Y. R.; Li, M. Z.; Liu, X. H., Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays, IEEE Trans Neural Networks, 17, 814-820 (2006)
[25] Boyd, S.; Ghaoui, E. L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM: SIAM Philadelphia · Zbl 0816.93004
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