Stability analysis for the generalized Cohen-Grossberg neural networks with inverse Lipschitz neuron activations

Computers and Mathematics with Applications

Volumn 57, Issue 9, 2009, Pages 1522-1536

  Nie, Xiaobing ^a   Cao, Jinde ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Cohen Grossberg neural networks; Global exponential stability; Inverse Lipschitz neuron activations; Linear matrix inequality; Nonsmooth behaved functions; Topological degree theory

Indexed keywords

CHEMICAL ACTIVATION; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; STABILITY; TIME VARYING NETWORKS; UNCERTAIN SYSTEMS; UNMANNED AERIAL VEHICLES (UAV);

COHEN-GROSSBERG NEURAL NETWORKS; GLOBAL EXPONENTIAL STABILITY; INVERSE LIPSCHITZ NEURON ACTIVATIONS; LINEAR MATRIX INEQUALITY; NONSMOOTH BEHAVED FUNCTIONS; TOPOLOGICAL DEGREE THEORY;

NEURAL NETWORKS;

EID: 63049101363     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.01.003     Document Type: Article

References (28)

1. Kosko B. Bidirectional associative memories. IEEE Trans. Syst. Man Cybern. 18 (1988) 49-60
2. Maundy B., and Ei-Masry E.I. A switched capacitor bidirectional associative memory. IEEE Trans. Circuits Syst. I 37 (1990) 1568-1572
3. Cohen M.A., and Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13 (1983) 815-826
4. Arik S. Global asymptotic stability of bidirectional associative memory neural networks with time delays. IEEE Trans. Neural Netw. 16 (2005) 580-586
5. Mohamad S. Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks. Phys. D 159 (2001) 233-251
6. Cao J., Ho D.W.C., and Huang X. LMI-based criteria for global robust stability of bidirectional associative memory networks with time delay. Nonlinear Anal. 66 (2007) 1558-1572
7. Huang C., and Huang L. Dynamics of a class of Cohen-Grossberg neural networks with time-varying delays. Nonlinear Anal.: RWA 8 (2007) 40-52
8. Yuan K., and Cao J. An analysis of global asymptotic st ability of delayed Cohen-Grossberg neural networks via nonsmooth analysis. IEEE Trans. Circuits Syst. I 52 (2005) 1854-1861
9. Song Q., and Wang Z. Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Phys. A 387 (2008) 3314-3326
10. Wang Z., Liu Y., Li M., and Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 17 (2006) 814-820
11. Yu W., Cao J., and Wang J. An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis. Neural Networks 20 (2007) 810-818
12. Cao J., and Song Q. Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19 (2006) 1601-1607
13. Yang F., Zhang C., and Wu D. Global stability analysis of impulsive BAM type Cohen-Grossberg neural networks with delays. Appl. Math. Comput. 186 (2007) 932-940
14. Wang Y., Cao J., and Huang G. LMI-based criteria for exponential robust stability of Cohen-Grossberg-type bidirectional associative memory neural networks with delays. J. Syst. and Control Engineering 222 (2008) 57-67
15. Jiang H., and Cao J. BAM-type Cohen-Grossberg neural networks with time delays. Math. Comput. Modelling 47 (2008) 92-103
16. Wu H., and Xue X. Stability analysis for neural networks with inverse Lipschitzian neuron activations and impulses. Appl. Math. Modelling 32 (2008) 2347-2359
17. H. Wu, Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations, Nonlinear Anal. RWA (in press)
18. Lu H., and He Z. Global exponential stability of delayed competitive neural networks with different time scales. Neural Networks 18 (2005) 243-250
19. Lu H., and Shun-ichi A. Global exponential stability of multitime scale competitive neural networks with nonsmooth functions. IEEE Trans. Neural Netw. 17 5 (2006) 1152-1164
20. Liu Y., Wang Z., and Liu X. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks 19 (2006) 667-675
21. 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 and Fractals 30 (2006) 886-896
22. Liu Y., Wang Z., and Liu X. On global exponential stability of generalized stochastic neural networks with mixed time-delays. Neurocomputing 70 (2006) 314-326
23. Liang J., Wang Z., Liu Y., and Liu X. Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances. IEEE Trans. Syst. Man Cybern. 38 (2008) 1073-1083
24. Liang J., Wang Z., and Liu X. Exponential synchronization of stochastic delayed discrete-time complex networks. Nonlinear Dynam. 53 (2008) 153-165
25. Rockafellar R.T., and Wets R.J.B. Variational Analysis (1998), Springer-Verlag, Berlin
26. Park J.H. A new stability analysis of delayed cellular neural networks. Appl. Math. Comput. 181 (2006) 200-205
27. Deimling K. Nonlinear Functional Analysis (1985), Springer-Verlag, Berlin
28. Miller P.K., and Michel A.N. Differential Equations (1982), Academic, New York