Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-20T11:33:24.508Z Has data issue: false hasContentIssue false

MIXED DELAY-DEPENDENT STABILITY OF HIGH-ORDER NEURAL NETWORKS BASED ON A WEAK COUPLING LMI SET

Published online by Cambridge University Press:  09 March 2010

MINGHAO LI
Affiliation:
College of Information Science and Technology, Donghua University, Shanghai, PR China (email: wnzhou@dhu.edu.cn)
WUNENG ZHOU*
Affiliation:
College of Information Science and Technology, Donghua University, Shanghai, PR China (email: wnzhou@dhu.edu.cn)
ZIWEI NI
Affiliation:
Department of Computer Science, Xiamen University, Xiamen, PR China (email: zwni@xmu.edu.cn)
MINGJUN WANG
Affiliation:
College of Information Science and Technology, Donghua University, Shanghai, PR China (email: wnzhou@dhu.edu.cn)
*
For correspondence; e-mail: wnzhou@dhu.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with the problem of discrete and distributed time-delay exponential stability for deterministic and uncertain stochastic high-order neural networks. The concept of a parameter weak coupling linear matrix inequality set (PWCLMIS) is developed. New results are derived in terms of PWCLMIS. Large mixed time delays can be obtained by using this approach. Furthermore, these results are more general than some previous existence results. Two numerical examples are given to show the merit of the approach.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2010

References

[1]Arik, S., “Global robust stability analysis of neural networks with discrete time delays”, Chaos Solitons Fractals 26 (2005) 14071414.CrossRefGoogle Scholar
[2]Artyomov, E. and Yadid-Pecht, O., “Modified high-order neural network for invariant pattern recognition”, Pattern Recognit. Lett. 26 (2005) 843851.CrossRefGoogle Scholar
[3]Blythe, S., Mao, X. and Liao, X., “Stability of stochastic delay neural networks”, J. Franklin Inst. 338 (2001) 481495.CrossRefGoogle Scholar
[4]Boyd, S., El Ghaoui, L., Feron, E. and Balakrishnan, V., Linear matrix inequalities in system and control theory (SIAM, Philadelphia, PA, 1994).CrossRefGoogle Scholar
[5]Cao, J. and Chen, T., “Globally exponentially robust stability and periodicity of delayed neural networks”, Chaos Solitons Fractals 22 (2004) 957963.Google Scholar
[6]Cao, J., Huang, D.-S. and Qu, Y., “Global robust stability of delayed recurrent neural networks”, Chaos Solitons Fractals 23 (2005) 221229.CrossRefGoogle Scholar
[7]Cao, J., Liang, J. and Lam, J., “Exponential stability of high-order bidirectional associative memory neural networks with time delays”, Phys. D 199 (2004) 425436.CrossRefGoogle Scholar
[8]Dembo, A., Farotimi, O. and Kailath, T., “High-order absolutely stable neural networks”, IEEE Trans. Circuits. Syst. 38 (1991) 5765.CrossRefGoogle Scholar
[9]Friedman, A., Stochastic differential equations and their applications, Volume 2 (Academic Press, New York, 1976).Google Scholar
[10]Gu, K., “An integral inequality in the stability problem of time-delay systems”, Proc. 39th IEEE Conf. on Decision and Control, Sydney, Australia, December 2000  (IEEE Computer Society, Los Alamitos, CA) 2805–2810.Google Scholar
[11]Hale, J. K., Theory of functional differential equations (Springer, New York, 1977).CrossRefGoogle Scholar
[12]Huang, H., Ho, D. W. C. and Lam, J., “Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays”, IEEE Trans. Circuits Syst.: Part II 52 (2005) 251255.CrossRefGoogle Scholar
[13]Karayiannis, N. B. and Venetsanopoulos, A. N., “On the training and performance of high-order neural networks”, Math. Biosci. 129 (1995) 143168.Google Scholar
[14]Li, M., Zhou, W., Wang, H., Chen, Y., Lu, R. and Lu, H., “Delay-dependent robust H control for uncertain stochastic systems”, Proc. 17th IFAC World Congress, Seoul, Korea, July 2008  (Curran Associates, New York, 2009) 6004–6009.Google Scholar
[15]Petersen, I. R., “A stabilization algorithm for a class of uncertain linear systems”, Systems Control Lett. 8 (1987) 351357.CrossRefGoogle Scholar
[16]Psaltis, D., Park, C. H. and Hong, J., “Higher order associative memories and their optical implementations”, Neural Networks 1 (1988) 143163.CrossRefGoogle Scholar
[17]Ren, F. and Cao, J., “LMI-based criteria for stability of high-order neural networks with time-varying delay”, Nonlinear Anal. Ser. B: Real World Appl. 7 (2006) 967979.CrossRefGoogle Scholar
[18]Ruan, S. and Filfil, R. S., “Dynamics of a two-neuron system with discrete and distributed delays”, Phys. D 191 (2004) 323342.CrossRefGoogle Scholar
[19]Wan, L. and Sun, J., “Mean square exponential stability of stochastic delayed Hopfield neural networks”, Phys. Lett. A 343 (2005) 306318.CrossRefGoogle Scholar
[20]Wang, Z., Fang, J. and Liu, X., “Global stability of stochastic high-order neural networks with discrete and distributed delays”, Chaos Solitons Fractals 36 (2008) 388396.CrossRefGoogle Scholar
[21]Wang, Z., Lauria, S., Fang, J. and Liu, X., “Exponential stability of uncertain stochastic neural networks with mixed time-delays”, Chaos Solitons Fractals 32 (2007) 6272.CrossRefGoogle Scholar
[22]Wang, Z., Liu, Y. and Liu, X., “On global asymptotic stability of neural networks with discrete and distributed delays”, Phys. Lett. A 345 (2005) 299308.CrossRefGoogle Scholar
[23]Wang, Z., Shu, H., Liu, Y., Ho, D. W. C. and Liu, X., “Robust stability analysis of generalized neural networks with discrete and distributed time delays”, Chaos Solitons Fractals 30 (2006) 886896.Google Scholar
[24]Wu, Z., Su, H., Chu, J. and Zhou, W., “New results on robust exponential stability for discrete recurrent neural networks with time-varying delays”, Neurocomputing 72 (2009) 33373342.Google Scholar
[25]Wu, Z., Su, H., Chu, J. and Zhou, W., “Improved result on stability analysis of discrete stochastic neural networks with time delay”, Phys. Lett. A 373 (2009) 15461552.CrossRefGoogle Scholar
[26]Xie, L., “Output feedback H control of systems with parameter uncertainty”, Internat. J. Control. 63 (1996) 741750.Google Scholar
[27]Zhao, H., “Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays”, Appl. Math. Comput. 154 (2004) 683695.Google Scholar
[28]Zhou, W., Lu, H. and Duan, C., “Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity”, Neurocomputing 72 (2009) 33573365.CrossRefGoogle Scholar