Globally asymptotic stability of a class of neutral-type neural networks with delays

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 36, Issue 5, 2006, Pages 1191-1195

  Cheng, Chao Jung ^a   Liao, Teh Liao ^b   Yan, Jun Juh ^c   Hwang, Chi Chuan ^b  

^a KUN SHAN UNIVERSITY   (Taiwan)

^b NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^c SHU TE UNIVERSITY   (Taiwan)

Author keywords

Cellular neural networks (CNNs); Cohen Grossberg neural networks (CGNNs); Hopfield neural networks (HNNs); Neutral type neural networks

Indexed keywords

ASYMPTOTIC STABILITY; DELAY CONTROL SYSTEMS; LYAPUNOV METHODS; MATHEMATICAL MODELS; STABILITY CRITERIA;

COHEN-GROSSBERG NEURAL NETWORKS; HOPFIELD NEURAL NETWORKS; NEUTRAL-TYPE NEURAL NETWORKS;

CELLULAR NEURAL NETWORKS;

ALGORITHM; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; LETTER; THEORETICAL MODEL; TIME;

ALGORITHMS; COMPUTER SIMULATION; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER); TIME FACTORS;

EID: 33749386815     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2006.874677     Document Type: Article

References (29)

1. M. Cohen and S. Grossberg, "Absolute stability of global pattern formation and parallel memory storage by competitive neural networks," IEEE Trans. Syst., Man, Cybern., vol. SMC-13, no. 5, pp. 815-826, Sep./Oct. 1983.
2. M. C. Carpenter, M. A. Cohen, S. Grossberg, T. Kohonen, E. Oja, and G. Palm, "Computing with neural network," Science, vol. 37, pp. 51-115, 1987.
3. N. Apostlou and R. E. King, "Neuronal state feedback learning of Cohen-Grossberg networks," Int. J. Circuit Theory Appl., vol. 27, no. 3, pp. 331-338, May 1999.
4. L. Wang and X. Zou, "Exponentially stability of Cohen-Grossberg neural networks," Neural Netw., vol. 15, no. 3, pp. 415-422, Apr. 2002.
5. S. Mohamad and K. Gopalsamy, "Exponential stability of continuous-time and discrete-time cellular neural networks with delays," Appl. Math. Comput., vol. 135, no. 1, pp. 17-38, Feb. 2003.
6. D. Zhou and J. Cao, "Globally exponential stability conditions for cellular neural networks with time-varying delays," Appl. Math. Comput., vol. 131, no. 2, pp. 487-496, Sep. 2002.
7. J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Nat. Acad. Sci. USA, vol. 79, no. 8, pp. 2554-2558, Apr. 1982.
8. L. O. Chua and L. Yang, "Cellular neural networks: Theory," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1257-1272, Oct. 1988.
9. B. Kosko, Neural Networks and Fuzzy Systems. Upper Saddle River, NJ: Prentice-Hall, 1992.
10. J. Cao, "Global stability conditions for delay CNNs," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 11, pp. 1330-1333, Nov. 2001.
11. S. Arik, "Stability analysis of delayed neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 7, pp. 1089-1092, Jul. 2000.
12. P. Baldi and A. F. Atiya, "How delays affect neural dynamics and learning," IEEE Trans. Neural Netw., vol. 5, no. 4, pp. 612-621, Jul. 1994.
13. R. Bellman and K. L. Cooke, Differential-Difference Equations. New York: Academic, 1963.
14. Z. Wang, J. Lam, and K. J. Burnham, "Stability analysis and observer design for neutral delay systems," IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 478-483, Mar. 2002.
15. I. D. Clarkson and D. P. Goodall, "On the stabilizability of imperfectly known nonlinear delay systems of the neutral type," IEEE Trans. Autom. Control, vol. 45, no. 12, pp. 2326-2331, Dec. 2000.
16. H. Ye, A. N. Michel, and K. Wang, "Qualitative analysis of Cohen-Grossberg neural networks with multiple delays," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 51, no. 3, pp. 2611-2618, Mar. 1995.
17. L. Wang and X. Zou, "Harmless delays in Cohen-Grossberg neural networks," Physica D, vol. 170, no. 2, pp. 162-173, Sep. 2002.
18. A. P. Tchangani, M. Dambrine, and J. P. Richard, "Stability, attraction domains, and ultimate boundedness for nonlinear neutral systems," Math. Comput. Simul., vol. 45, no. 3/4, pp. 291-298, Feb. 1998.
19. A. Bellen, N. Guglielmi, and A. E. Ruehli, "Methods for linear systems of circuit delay differential equations of neutral type," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 46, no. 1, pp. 212-215, Jan. 1999.
20. R. P. Agarwal and S. R. Grace, "Asymptotic stability of differential systems of neutral type," Appl. Math. Lett., vol. 13, no. 8, pp. 15-19, Nov. 2000.
21. R. P. Agarwal and S. R. Grace, "Asymptotic stability of certain neutral differential equations," Math. Comput. Model., vol. 31, no. 8, pp. 9-15, Apr. 2000.
22. Z. Yi, "Stability of neutral Lotka-Volterra systems," J. Math. Anal. Appl., vol. 199, no. 2, pp. 391-402, Apr. 1996.
23. J. H. Li, A. N. Michel, and W. Porod, "Qualitative analysis and synthesis of a class of neural networks," IEEE Trans. Circuits Syst., vol. 35, no. 8, pp. 976-986, Aug. 1988.
24. M. Joy, "On the global convergence of a class of functional differential equations with applications in neural network theory," J. Math. Anal. Appl., vol. 232, no. 1, pp. 61-81, Apr. 1999.
25. S. Xu, J. Lam, W. C. Ho, and Y. Zou, "Delay-dependent exponential stability for a class of neural networks with time delays," J. Comput. Appl. Math., vol. 183, no. 1, pp. 16-28, Nov. 2005.
26. S. Senan and S. Arik, "New results for exponential stability of delayed cellular neural networks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 3, pp. 154-158, Mar. 2005.
27. V. Singh, "A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 223-225, Jan. 2004.
28. C. H. Lien, "Asymptotic criterion for neutral systems with multiple time delays," Electron. Lett., vol. 35, no. 10, pp. 850-852, May 1999.
29. J. K. Hale and S. M. Verduyn, Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993.