LMI-based criteria for stability of high-order neural networks with time-varying delay

Nonlinear Analysis: Real World Applications

Volumn 7, Issue 5, 2006, Pages 967-979

  Ren, Fengli ^a   Cao, Jinde ^a  

^a SOUTHEAST UNIVERSITY   (China)

Author keywords

Global exponential stability; High order neural networks; Linear matrix inequality; Lyapunov functional; Time varying delay

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; MATRIX ALGEBRA; NEURAL NETWORKS; PROBLEM SOLVING;

GLOBAL EXPONENTIAL STABILITY; HIGH ORDER NEURAL NETWORKS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONALS; TIME VARYING DELAY;

TIME VARYING NETWORKS;

EID: 33745126296     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2005.09.001     Document Type: Article

References (28)

1. Abu-Mostafa Y., and Jacques J. Information capacity of the Hopfield model. IEEE Trans. Inform. Theory 31 (1985) 461-464
2. Arik S. An analysis of exponential stability of delayed neural networks with time varying delays. Neural Networks 17 7 (2004) 1027-1031
3. Baldi P. Neural networks, orientations of the hypercube and algebraic threshold functions. IEEE Trans. Inform. Theory 34 (1998) 523-530
4. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadephia, PA
5. Bruk J., and Sanz J. A study on neural networks. Int. J. Intelligent Syst. 3 (1988) 57-59
6. Cao J., and Ho D.W.C. A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach. Chaos, Solitons and Fractals 24 (2005) 1317-1329
7. Cao J., Liang J., and Lam J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199 3-4 (2004) 425-436
8. Cao J., and Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I 50 1 (2003) 34-44
9. Cao J., and Wang J. Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 52 5 (2005) 920-931
10. Chen T., and Rong L. Delay-independent stability analysis of Cohen-Grossberg neural networks. Phys. Lett. A 317 5-6 (2003) 436-449
11. 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
12. Dembo A., Farotimi O., and Kailath T. High-order absolutely stable neural networks. IEEE Trans. Circuits Syst. 38 1 (1991) 57-65
13. Hale J.K., and Lunel S.M.V. Introduction to Functional Differential Equations (1991), Springer-Verlag, New York
14. Ho D.W.C., Lam J., Xu J., and Tam H.K. Neural computation for robust approximate pole assignment. Neurocomputing 25 (1999) 191-211
15. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. USA, Biophysics 81 (1984) 3088-3092
16. Huang X., Cao J., and Huang D. LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks. Chaos, Solitons and Fractals 24 (2005) 885-898
17. Kamp Y., and Hasler M. Recursive neural networks for associative memory (1990), Wiley, New York
18. Kosmatopoulos E.B., and Christodoulou M.A. Structural properties of gradient recurrent higher-order neural networks. IEEE Trans. Circuits Syst. II 42 (1995) 592-603
19. Kosmatopoulos E.B., Polycarpou M.M., Christodoulou M.A., and Ioannou P.A. High-order neural network structures for identification on dynamical systems. IEEE Trans. Neural Networks 6 (1995) 422-431
20. Li C., Liao X., and Rong Z. Global robust asymptotical stability of muti-delayed interval neural networks: an LMI approach. Phys. Lett. A 328 (2004) 452-462
21. Cao J., and Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 52 2 (2005) 417-426
22. McEliece R.J., Posner E.C., Rodemich E.R., and Venkatesh S.S. The capacity of the Hopfield associative memory. IEEE Trans. Inform. Theory 33 (1983) 461-482
23. Peretto P., and Niez J.J. Long term memory storage capacity of multiconnected neural networks. Biol. Cybern. 54 (1986) 53-63
24. Personnaz L., Guyon I., and Dreyfus G. High-order neural networks: Information storage without errors. Europhysics Lett. 4 8 (1987) 863-867
25. Psaltis D., Park C.H., and Hong J. Higher-order associative memories and their optical implementations. Neural Networks 1 2 (1988) 149-163
26. Sanchez E.N., and Perez J.P. Input-to-state stability (ISS) analysis for dynamic NN. IEEE Trans. Circuits Syst. I 46 (1999) 1395-1398
27. Simpson P.K. Higher-ordered and intraconnected bidirectional associative memories. IEEE Trans. Syst. Man Cybern. 20 (1990) 637-653
28. Xu B., Liu X., and Liao X. Global asymptotic stability of high-order Hopfield type neural networks with time delays. Comput. Math. Appl. 45 (2003) 1729-1737