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Singh, Vimal

Improved global robust stability criterion for delayed neural networks. (English) Zbl 1142.93400

Chaos Solitons Fractals 31, No. 1, 224-229 (2007).
Summary: A criterion for the uniqueness and global robust stability of the equilibrium point of interval Hopfield-type delayed neural networks is presented. The criterion is a marked improvement over a recent criterion due to Cao, Huang and Qu.

Cited in 12 Documents

MSC:

93D09 Robust stability
34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
93C15 Control/observation systems governed by ordinary differential equations

Keywords:

global robust stability; Hopfield-type delayed neural networks; global asymptotic stability

Software:

LMI toolbox
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\textit{V. Singh}, Chaos Solitons Fractals 31, No. 1, 224--229 (2007; Zbl 1142.93400)
Full Text: DOI

References:

[1] Roska, T.; Wu, C. W.; Balsi, M.; Chua, L. O., Stability and dynamics of delay-type general and cellular neural networks, IEEE Trans Circuits Syst I, 39, 6, 487-490 (1993) · Zbl 0775.92010
[2] Civalleri, P. P.; Gilli, M.; Pandolfi, L., On stability of cellular neural networks with delay, IEEE Trans Circuits Syst I, 40, 3, 157-164 (1993) · Zbl 0792.68115
[3] Roska, T.; Wu, C. W.; Chua, L. O., Stability of cellular neural networks with dominant nonlinear and delay-type templates, IEEE Trans Circuits Syst I, 40, 4, 270-272 (1993) · Zbl 0800.92044
[4] Gopalsamy, K.; He, X. Z., Stability in asymmetric Hopfield networks with transmission delays, Physica D, 76, 4, 344-358 (1994) · Zbl 0815.92001
[5] Ye, H.; Michel, A. N.; Wang, K. N., Global stability and local stability of Hopfield neural networks with delays, Phys Rev E, 50, 5, 4206-4213 (1994)
[6] Forti, M.; Tesi, A., New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans Circuits Syst I, 42, 7, 354-366 (1995) · Zbl 0849.68105
[7] Liao, X.; Yu, J., Robust stability for interval Hopfield neural networks with time delay, IEEE Trans Neural Networks, 9, 5, 1042-1046 (1998)
[8] Cao, J.; Zhou, D., Stability analysis of delayed cellular neural networks, Neural Networks, 11, 9, 1601-1605 (1998)
[9] Arik, S.; Tavsanoglu, V., On the global asymptotic stability of delayed cellular neural networks, IEEE Trans Circuits Syst I, 47, 4, 571-574 (2000) · Zbl 0997.90095
[10] Takahashi, N., A new sufficient condition for complete stability of cellular neural networks with delay, IEEE Trans Circuits Syst I, 47, 6, 793-799 (2000) · Zbl 0964.94008
[11] Liao, T. L.; Wang, F. C., Global stability for cellular neural networks with time delay, IEEE Trans Neural Networks, 11, 6, 1481-1484 (2000)
[12] Cao, J., A set of stability criteria for delayed cellular neural networks, IEEE Trans Circuits Syst I, 48, 4, 494-498 (2001) · Zbl 0994.82066
[13] Zhang, Q.; Ma, R.; Xu, J., Stability of cellular neural networks with delay, Electron Lett, 37, 9, 575-576 (2001)
[14] Yi, Z.; Heng, P.; Leung, K. S., Convergence analysis of cellular neural networks with unbounded delay, IEEE Trans Circuits Syst I, 48, 6, 680-687 (2001) · Zbl 0994.82068
[15] Chen, T., Global exponential stability of delayed Hopfield neural networks, Neural Networks, 14, 8, 977-980 (2001)
[16] Cao, J., Global stability conditions for delayed CNNs, IEEE Trans Circuits Syst I, 48, 11, 1330-1333 (2001) · Zbl 1006.34070
[17] Liao, X.; Wong, K.; Wu, Z.; Chen, G., Novel robust stability for interval-delayed Hopfield neural networks, IEEE Trans Circuits Syst I, 48, 11, 1355-1359 (2001) · Zbl 1006.34071
[18] Liao, X.; Chen, G.; Sanchez, E. N., LMI-based approach for asymptotically stability analysis of delayed neural networks, IEEE Trans Circuits Syst I, 49, 7, 1033-1039 (2002) · Zbl 1368.93598
[19] Arik, S., An improved global stability result for delayed cellular neural networks, IEEE Trans Circuits Syst I, 49, 8, 1211-1214 (2002) · Zbl 1368.34083
[20] Liao, X.; Chen, G.; Sanchez, E. N., Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Networks, 15, 7, 855-866 (2002)
[21] Arik, S., An analysis of global asymptotic stability of delayed cellular neural networks, IEEE Trans Neural Networks, 13, 5, 1239-1242 (2002)
[22] Cao, J.; Wang, J., Global asymptotic stability of recurrent neural networks with Lipschitz-continuous activation functions and time-varying delays, IEEE Trans Circuits Syst I, 50, 1, 33-44 (2003)
[23] Arik, S., Global robust stability of delayed neural networks, IEEE Trans Circuits Syst I, 50, 1, 156-160 (2003) · Zbl 1368.93490
[24] Zhang, Q.; Ma, R.; Wang, C.; Xu, J., On the global stability of delayed neural networks, IEEE Trans Automat Contr, 48, 5, 399-405 (2003)
[25] Arik, S., Global asymptotic stability of a larger class of neural networks with constant time delays, Phys Lett A, 311, 6, 504-511 (2003) · Zbl 1098.92501
[26] Lu, W.; Rong, L.; Chen, T., Global convergence of delayed neural network systems, Int J Neural Systems, 13, 3, 193-204 (2003)
[27] Zhang, Q.; Wei, X. P.; Xu, J., Global asymptotic stability of Hopfield neural networks with transmission delays, Phys Lett A, 318, 4-5, 399-405 (2003) · Zbl 1030.92003
[28] Qiao, H.; Peng, J.; Xu, Z.-B.; Zhang, B., A reference model approach to stability analysis of neural networks, IEEE Trans Syst Man Cybern B, 33, 6, 925-936 (2003)
[29] Singh, V., A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks, IEEE Trans Neural Networks, 15, 1, 223-225 (2004)
[30] Singh, V., Robust stability of cellular neural networks with delay: linear matrix inequality approach, IEE Proc—Contr Theory Appl, 151, 1, 125-129 (2004)
[31] Singh, V., Global asymptotic stability of cellular neural networks with unequal delays: LMI approach, Electron Lett, 40, 9, 548-549 (2004)
[32] Cao, J.; Chen, T., Globally exponentially robust stability and periodicity of delayed neural networks, Chaos, Solitons & Fractals, 22, 4, 957-963 (2004) · Zbl 1061.94552
[33] Cao, J.; Huang, D.-S.; Qu, Y., Global robust stability of delayed recurrent neural networks, Chaos, Solitons & Fractals, 23, 1, 221-229 (2005) · Zbl 1075.68070
[34] Singh, V., Global robust stability of delayed neural networks: an LMI approach, IEEE Trans Circuits Syst II, 52, 1, 33-36 (2005)
[35] Singh, V., A novel global robust stability criterion for neural networks with delay, Phys Lett A, 337, 4-6, 369-373 (2005) · Zbl 1136.34346
[36] Cao, J.; Ho, D. W.C., A general framework for global asymptotic stability of delayed neural networks based on LMI approach, Chaos, Solitons & Fractals, 24, 5, 1317-1329 (2005) · Zbl 1072.92004
[37] He, Y.; Wang, Q. G.; Zheng, W. X., Global robust stability for delayed neural networks with polytopic type uncertainties, Chaos, Solitons & Fractals, 26, 5, 1349-1354 (2005) · Zbl 1083.34535
[38] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM: SIAM Philadelphia (PA) · Zbl 0816.93004
[39] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M., LMI control toolbox—for use with Matlab (1995), The MATH Works Inc.: The MATH Works Inc. Natick (MA)
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