Stability for neural networks with time-varying delays via some new approaches

IEEE Transactions on Neural Networks and Learning Systems

Volumn 24, Issue 2, 2013, Pages 181-193

  Kwon, Oh Min ^a   Park, Myeong Jin ^a   Lee, Sang Moon ^b   Park, Ju H ^c   Cha, Eun Jong ^a  

^a Chungbuk National University   (South Korea)

^b Daegu University   (South Korea)

^c Yeungnam University   (South Korea)

Author keywords

Lyapunov method; Neural networks; Stability; Time varying delays

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; NEURAL NETWORKS; TIME VARYING CONTROL SYSTEMS;

ACTIVATION FUNCTIONS; DELAY DEPENDENT STABILITY CRITERION; LYAPUNOV-KRASOVSKII FUNCTIONALS; NEW APPROACHES; TIME-VARYING DELAY;

STABILITY CRITERIA;

ARTIFICIAL NEURAL NETWORK; TIME;

NEURAL NETWORKS (COMPUTER); TIME FACTORS;

EID: 84885431392     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2012.2224883     Document Type: Article

References (39)

1. L. O. Chua and L. Yang, "Cellular neural networks: Applications," IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1273-1290, Oct. 1988.
2. A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing. Hoboken, NJ: Wiley, 1993.
3. G. Joya, M. A. Atencia, and F. Sandoval, "Hopfield neural networks for optimization: Study of the different dynamics," Neurocomputing, vol. 43, nos. 1-4, pp. 219-237, 2002. (Pubitemid 34041235)
4. W. J. Li and T. Lee, "Hopfield neural networks for affine invariant matching," IEEE Trans. Neural Netw., vol. 12, no. 6, pp. 1400-1410, Nov. 2001. (Pubitemid 33106045)
5. T. Ensari and S. Arik, "Global stability of a class of neural networks with time-varying delay," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 3, pp. 126-130, Mar. 2005. (Pubitemid 40429271)
6. O. Faydasicok and S. Arik, "Robust stability analysis of a class of neural networks with discrete time delays," Neural Netw., vols. 29-30, pp. 52- 59, May 2012.
7. S. Xu, J. Lam, and D. W. C. Ho, "Novel global robust stability criteria for interval neural networks with multiple time-varying delays," Phys. Lett. A, vol. 342, no. 4, pp. 322-330, 2005. (Pubitemid 40884455)
8. O. M. Kwon and J. H. Park, "Exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays," Appl. Math. Comput., vol. 203, no. 2, pp. 813-823, 2008.
9. O. M. Kwon and J. H. Park, "New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays," Appl. Math. Comput., vol. 205, no. 1, pp. 417-427, 2008.
10. P. Balasubramaniam and S. Lakshmanan, "Delay-range dependent stability criteria for neural networks with Markovian jumping parameters," Nonlinear Anal., Hybrid Syst., vol. 3, no. 4, pp. 749-756, 2009.
11. P. Balasubramaniam, S. Lakshmanan, and R. Rakkiyappan, "Delayinterval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties," Neurocomputing, vol. 72, nos. 16- 18, pp. 3675-3682, 2009.
12. K. Mathiyalagan, R. Sakthivel, and S. M. Anthoni, "New robust passivity criteria for stochastic fuzzy BAM neural networks with time-varying delays," Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 3, pp. 1392-1407, 2012.
13. Z. G. Wu, P. Shi, H. Su, and J. Chu, "Stability and dissipativity analysis of static neural networks with time delay," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 2, pp. 199-210, Feb. 2012.
14. Z. G. Wu, J. Lam, P. Shi, H. Su, and J. Chu, "Stability analysis for discrete-time Markovian jump neural networks with mixed time-delays," Expert Syst. Appl., vol. 39, no. 6, pp. 6174-6181, Feb. 2012.
15. Y. Liu, Z. Wang, and X. Liu, "Global exponential stability of generalized recurrent neural networks with discrete and distributed delays," Neural Netw., vol. 19, no. 5, pp. 667-675, 2006.
16. K. Mathiyalagan, R. Sakthivel, and S. M. Anthoni, "Exponential stability result for discrete-time stochastic fuzzy uncertain neural networks," Phys. Lett. A, vol. 376, nos. 8-9, pp. 901-912, 2012.
17. M. Wu, F. Liu, P. Shi, Y. He, and R. Yokoyama, "Exponential stability analysis for neural networks with time-varying delay," IEEE Trans. Syst., Man Cybern. B, Cybern., vol. 38, no. 4, pp. 1152-1156, Aug. 2008.
18. H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability of recurrent neural networks with multiple time-varying delays," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 855-873, May 2008. (Pubitemid 351728821)
19. X. L. Zhu and G. H. Yang, "New delay-dependent stability results for neural networks with time-varying delay," IEEE Trans. Neural Netw., vol. 19, no. 10, pp. 1783-1791, Oct. 2008.
20. O. M. Kwon, J. W. Kwon, and S. H. Kim, "New results on stability criteria for neural networks with time-varying delays," Chin. Phys. B, vol. 20, no. 5, pp. 050505-1-050505-5, 2011.
21. T. Li, W. X. Zheng, and C. Lin, "Delay-slope-dependent stability results of recurrent neural networks," IEEE Trans. Neural Netw., vol. 22, no. 12, pp. 2138-2143, Dec. 2011.
22. Y. Zhang, D. Yue, and E. Tian, "New stability criteria of neural networks with interval time-varying delays: A piecewise delay method," Appl. Math. Comput., vol. 208, no. 1, pp. 249-259, 2009.
23. O. M. Kwon and J. H. Park, "Improved delay-dependent stability criterion for neural networks with time-varying delays," Phys. Lett. A, vol. 373, no. 5, pp. 529-535, Jan. 2009.
24. J. Tian and X. Xie, "New asymptotic stability criteria for neural networks with time-varying delay," Phys. Lett. A, vol. 374, no. 7, pp. 938-943, 2010.
25. J. Tian and S. Zhong, "Improved delay-dependent stability criterion for neural networks with time-varying delay," Phys. Lett. A, vol. 373, no. 5, pp. 529-535, 2009.
26. S.-P. Xiao and X.-M. Zhang, "New globally asymptotic stability criteria for delayed cellular neural networks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 56, no. 8, pp. 659-663, Aug. 2009.
27. Y. Wang, C. Yang, and Z. Zuo, "On exponential stability analysis for neural networks with time-varying delays and general activation functions," Commun. Nonlinear Sci. Numer. Simul., vol. 17, no. 3, pp. 1447-1459, 2012.
28. H. Zhang, Z. Liu, G.-B. Huang, and Z. Wang, "Novel weighting-delaybased stability criteria for recurrent neural netowrks with time-varying delay," IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 91-106, Jan. 2010.
29. C.-D. Zheng, H. Zhang, and Z. Wang, "An augmented LKF approach involving derivative information of both state and delay," IEEE Trans. Neural Netw., vol. 21, no. 7, pp. 1100-1109, Jul. 2010.
30. C.-D. Zheng, Q.-H. Shan, and Z. Wang, "Novel stability criterion for cellular neural networks: An improved Gu's discretized LKF approach," J. Franklin Inst., vol. 349, no. 1, pp. 25-41, 2012.
31. M. Morita, "Associative memory with nonmonotone dynamics," Neural Netw., vol. 6, no. 1, pp. 115-126, 1993. (Pubitemid 23613240)
32. Y. Ariba and F. Gouaisbaut, "An augmented model for robust stability analysis of time-varying delay systems," Int. J. Control, vol. 82, no. 9, pp. 1616-1626, 2009.
33. P. G. Park, J. W. Ko, and C. Jeong, "Reciprocally convex approach to stability of systems with time-varying delays," Automatica, vol. 47, no. 1, pp. 235-238, 2011.
34. S. H. Kim, P. Park, and C. Jeong, "Robust H∞ stabilisation of networked control systems with packet analyser," IET Control Theory Appl., vol. 4, no. 9, pp. 1828-1837, Sep. 2010.
35. I. E. Köse, F. Jabbari, and W. E. Schmitendorf, "A direct characterization of L2-gain controllers for LPV systems," IEEE Trans. Auto. Control, vol. 43, no. 9, pp. 1302-1307, Sep. 1998. (Pubitemid 128736525)
36. K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. IEEE Conf. Decision Control, Dec. 2000, pp. 2805- 2810. (Pubitemid 32528463)
37. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA: SIAM, 1994.
38. R. E. Skelton, T. Iwasaki, and K. M. Grigoradis, A Unified Algebraic Approach to Linear Control Design. New York: Taylor & Francis, 1997.
39. Z.-G. Wu, J. H. Park, H. Su, and J. Chu, "New results on exponential passivity of neural networks with time-varying delays," Nonlinear Anal.- Real World Appl., vol. 13, no. 4, pp. 1593-1599, 2012.