LMI approach for global periodicity of neural networks with time-varying delays

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 52, Issue 7, 2005, Pages 1451-1458

  Rong, Libin ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Exponential stability; Linear matrix inequality (LMI); Neural networks; Periodic solutions; Time varying delays

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; MATRIX ALGEBRA; TIME VARYING CONTROL SYSTEMS;

EXPONENTIAL STABILITY; LINEAR MATRIX INEQUALITIES (LMI); PERIODIC SOLUTIONS; TIME VARYING DELAYS;

NEURAL NETWORKS;

EID: 23144431801     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2005.851704     Document Type: Article

References (29)

1. B. Chen and J. Wang, "Global exponential periodicity and global exponential stability of a class of recurrent neural networks," Phys. Lett. A, vol. 329, pp. 36-48, 2004.
2. S. Arik, "Stability analysis of delayed neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 10, pp. 1089-1092, Oct. 2000.
3. S. Arik and V. Tavsanoglu, "On the global asymptotic stability of delayed cellular neural networks," IEEE Trans. Circuits Syst. I. Fundam. Theory Appl., vol. 47, no. 4, pp. 571-574, Apr. 2000.
4. J. Cao, "On exponential stability and periodic solution of cnns with delay," Phys. Lett., vol. 267, pp. 312-318, 2000.
5. J. Cao, "Global stability conditions for delayed cnns," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 11, pp. 1330-1333, Nov. 2001.
6. T. Chen and L. Rong, "Robust global exponential stability of cohengrossberg neural networks with time delays," IEEE Trans. Neur. Netw., vol. 15, no. 1, pp. 203-206, Feb. 2004.
7. T. Chen and L. Rong, "Delay-independent stability of cohen-grossberg nerual networks," Phys. Lett. A, vol. 317, pp. 436-449, 2003.
8. P. V. D. Driessche and X. Zou, "Global attractivity in delayed hopfield neural networks models," in SIAM J. Applied Math., vol. 58, 1998, pp. 1878-1890.
9. M. Forti and A. Tesi, "New conditions for global stability of neural networks with Application to liner and quadratic programming problems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42, no. 3, pp. 354-366, Mar. 1995.
10. X. Liao, G. Chen, and E. Sanchez, "Delay-dependent exponential stability analysis of delayed neural networks: An LMI approch," Neur. Netw., vol. 15, pp. 855-866, 2002.
11. X. Liao, G. Chen, and E. Sanchez, "LMI-based approch for asymptotic stability analysis of delayed neural networks," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 7, pp. 1033-1039, Jul. 2002.
12. W. Lu, L. Rong, and T. Chen, "Global convergence of delayed neural network systems," Int. J. Neur. Syst., vol. 13, no. 3, pp. 193-204, 2003.
13. L. Rong, W. Lu, and T. Chen, "Global exponential stability in hopfield and bidirectional associative memory neural networks with time delays," Chin. Ann. Math., vol. 25, no. 2, pp. 255-262, 2004.
14. V. Singh, "A generlized LMI-based Approach to the global asyptotic stability of delayed cellular neural networks," IEEE Trans. Neur. Netw., vol. 15, no. 1, pp. 223-225, Feb. 2004.
15. Y. Zhang, P. Heng, and K. Leung, "Convergence analysis of cellular neural networks with unbounded delay," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 6, pp. 680-687, Jun. 2001.
16. K. Gopalsamy and X. He, "Stability in asymmetric hopfield nets with Transmission delays," Phys. D, vol. 76, pp. 344-358, 1994.
17. M. Joy, "On the global convergence of class of functional differential equations with Applications in neural network theory," J. Math. Anal. Appl., vol. 232, pp. 61-81, 1999.
18. C. Sun and C. Feng, "Exponential periodicity and stability of delayed neural networks," Math. Comp. Simul., vol. 66, pp. 469-478, 2004.
19. Z. Liu, A. Chen, J. Co, and L. Hung, "Existence and global exponential stability of periodic solution for bam neural networks with periodic coefficients and time-varying delays," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 10, pp. 1162-1173, Oct. 2003.
20. Y. Li, "Existence and stability of periodic solutions for cohen-grossberg neural networks with multiple delays," Chaos, Solitons, Fractals, vol. 20, pp. 459-466, 2004.
21. S. Boyd, L. Ghoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
22. R. Gaines and J. Mawhin, Coincidence Degree and Nonlinear Differential Equations. Berlin, Germany: Springer-Verlag, 1977.
23. N. Rouche and J. Mawhin, Ordinary Differential Equations: Stability and Periodic Solutions, R. Gaines, Ed. Boston, MA: Pitman, 1980.
24. H. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice-Hall, 2002.
25. S. Arik, "An analysis of global asymptotic stability of delayed cellular neural networks," IEEE Trans. Neur. Netw., vol. 13, no. 5, pp. 1239-1242, Oct. 2002.
26. V. Singh, "Robust stability of cellular neural networks with delay: Linear matrix inequality Approach," Proc. IEE, Contr. Theory Appl., vol. 151, no. 1, pp. 125-129, 2004.
27. E. Yucel and S. Arik, "New exponential stability results for delayed neural networks with time varying delays," Phys. D, vol. 191, pp. 314-322, 2004.
28. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI control Toolbox-for Use with Matlab. Natick, MA: The Math Works Inc., 1995.
29. J. Cao and Q. Li, "On the exponential stability and periodic solutions of delayed cellular neural networks," J. Math. Anal. Appl., vol. 252, 2000.