Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

Neural Networks

Volumn 19, Issue 5, 2006, Pages 667-675

  Liu, Yurong ^a   Wang, Zidong ^b   Liu, Xiaohui ^b  

^a YANGZHOU UNIVERSITY   (China)

^b BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Discrete and distributed delays; Generalized recurrent neural networks; Global asymptotic stability; Global exponential stability; Linear matrix inequality; Lyapunov Krasovskii functional

Indexed keywords

ACTIVATION ANALYSIS; COMPUTER SIMULATION; PARAMETER ESTIMATION; PROBLEM SOLVING; STABILITY;

DISCRETE AND DISTRIBUTED DELAYS; GENERALIZED RECURRENT NEURAL NETWORKS; GLOBAL ASYMPTOTIC STABILITY; GLOBAL EXPONENTIAL STABILITY; LINEAR MATRIX INEQUALITY; LYAPUNOV-KRASOVSKII FUNCTIONAL;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; FUNCTIONAL ASSESSMENT; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; PRIORITY JOURNAL; SIMULATION; TIME;

ARTIFICIAL INTELLIGENCE; HUMANS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); NEURONS; NONLINEAR DYNAMICS; PATTERN RECOGNITION, AUTOMATED; TIME FACTORS;

EID: 33646511197     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2005.03.015     Document Type: Article

References (29)

1. Arik S. Stability analysis of delayed neural networks. IEEE Transactions on Circuits Systems-I 47 (2000) 1089-1092
2. Baldi P., and Atiya A.F. How delays affect neural dynamics and learning. IEEE Transactions on Neural Networks 5 (1994) 612-621
3. Boyd S., El Ghaoui L., Feron E., and Balakrishnan V. Linear matrix inequalities in system and control theory (1994), SIAM, Philadephia
4. Cao J. Periodic oscillation and exponential stability of delayed CNNs. Physics Letters A 270 (2000) 157-163
5. Cao J., Huang D.-S., and Qu Y. Global robust stability of delayed recurrent neural networks. Chaos, Solitons & Fractals 23 1 (2005) 221-229
6. Cao J., and Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I 50 1 (2003) 34-44
7. Cao J., and Wang J. Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays. Neural Networks 17 3 (2004) 379-390
8. Chen B., and Wang J. Global exponential periodicity and global exponential stability of a class of recurrent neural networks. Physics Letters A 329 1/2 (2004) 36-48
9. Gahinet P., Nemirovsky A., Laub A.J., and Chilali M. LMI control toolbox: for use with Matlab (1995), The MATH Works, Inc., Natick, MA
10. Gu, K. (2000). An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference on decision and control, Sydney, Australia, December 2000 (pp. 2805-2810).
11. Hale J.K. The theory of functional differential equations (1977), Springer, New York
12. Hu S., and Wang J. Absolute exponential stability of a class of continuous-time recurrent neural networks. IEEE Transactions on Neural Networks 14 1 (2003) 35-45
13. Huang H., and Cao J. On global asymptotic stability of recurrent neural networks with time-varying delays. Applied Mathematics and Computation 142 1 (2003) 143-154
14. Liang J., and Cao J. Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays. Physics Letters A 318 1/2 (2003) 53-64
15. Liang J., and Cao J. Global asymptotic stability of bi-directional associative memory networks with distributed delays. Applied Mathematics and Computation 152 (2004) 415-424
16. Liao X., Chen G., and Sanchez E.N. LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Transactions on Circuits Systems-I 49 (2002) 1033-1039
17. Liao X., Wong K.W., and Li C. Global exponential stability for a class of generalized neural networks with distributed delays. Nonlinear Analysis: Real World Applications 5 (2004) 527-547
18. Nesterov Y., and Nemirovsky A. Interior point polynomial methods in convex programming: theory and applications (1993), SIAM, Philadelphia, PA
19. Principle J.C., Kuo J.-M., and Celebi S. An analysis of the gamma memory in dynamic neural networks. IEEE Transactions on Neural Networks 5 2 (1994) 337-361
20. Ruan S., and Filfil R.S. Dynamics of a two-neuron system with discrete and distributed delays. Physica D 191 (2004) 323-342
21. Tank D.W., and Hopfield J.J. Neural computation by concentrating information in time. Proceedings of the National Academy of Sciences of the United States of America 84 (1987) 1896-1991
22. Wang Z., and Ho D.W.C. Filtering on nonlinear time-delay stochastic systems. Automatica 39 1 (2003) 101-109
23. Wang Z., Ho D.W.C., and Liu X. A note on the robust stability of uncertain stochastic fuzzy systems with time-delays. IEEE Transactions on Systems, Man and Cybernetics-Part A 34 4 (2004) 570-576
24. Wang Z., Ho D.W.C., and Liu X. State estimation for delayed neural networks. IEEE Transactions on Neural Networks 16 1 (2005) 279-284
25. Xu S., Lam J., and Ho D.W.C. Global robust exponential stability analysis for interval recurrent neural networks. Physics Letters A 325 (2004) 124-133
26. Zeng Z., Wang J., and Liao X. Global exponential stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I 50 10 (2003) 1353-1358
27. Zhang Q., Wei X., and Xu J. Global exponential stability of Hopfield neural networks with continuously distributed delays. Physics Letters A 315 6 (2003) 431-436
28. Zhao H. Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Networks 17 (2004) 47-53
29. Zhao H. Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Applied Mathematics and Computation 154 (2004) 683-695