Delay-dependent robust stability analysis of uncertain stochastic neural networks with discrete interval and distributed time-varying delays

Neurocomputing

Volumn 72, Issue 13-15, 2009, Pages 3231-3237

  Balasubramaniam, P ^a   Rakkiyappan, R ^a  

^a GANDHIGRAM RURAL UNIVERSITY   (India)

Author keywords

Delay interval dependent stability; Linear matrix inequality; Lyapunov Krasovskii functional; Stochastic neural networks

Indexed keywords

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; NEURAL NETWORKS; NONLINEAR CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); STABILITY; STOCHASTIC SYSTEMS; TIME DELAY; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

DELAY-DEPENDENT ROBUST STABILITY; DEPENDENT STABILITY; DISCRETE TIME-VARYING DELAYS; INTERVAL TIME-VARYING DELAYS; LYAPUNOV-KRASOVSKII FUNCTIONALS; STOCHASTIC NEURAL NETWORK; STOCHASTIC STABILITY THEORY; UPPER AND LOWER BOUNDS;

STABILITY CRITERIA;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CONTROLLED STUDY; MATHEMATICAL PARAMETERS; PRIORITY JOURNAL; STOCHASTIC MODEL; THEORY; UNCERTAINTY;

EID: 78049249611     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2009.02.007     Document Type: Article

References (26)

1. S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, NJ, 1998.
2. A. Cichoki, R. Unbehauen, Neural Networks for Optimization and Signal Processing, Wiley, Chichester, 1993.
3. T.L. Liao, F.C. Wang, Global stability for cellular neural networks with time delay, IEEE Trans. Neural Networks 11 (2000) 1481-1484.
4. S. Arik, Global asymptotic stability of a class of dynamical neural networks, IEEE Trans. Circuits Syst. I 47 (2000) 568-571.
5. J. Cao, J. Wang, Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Trans. Circuits Syst. I 50 (2003) 33-44.
6. V. Singh, A generalised LMI-based approach to the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Neural Networks 15 (2004) 223-225.
7. S. Xu, J. Lam, D.W.C. Ho, A new LMI condition for delay-dependent asymptotic stability of delay Hopfield neural network, IEEE Trans. Circuits Syst. II, Exp. Briefs 53 (2006) 230-234.
8. J.H. Park, A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays, Chaos Solitons Fractals 33 (2007) 436-442.
9. C.-H. Lien, L.-Y. Chung, Global asymptotic stability for cellular neural networks with discrete and distributed delays, Chaos Solitons Fractals 34 (2007) 1213-1219.
10. Y. He, G.P. Liu, D. Rees, New delay-dependent stability criteria for neural networks with time-varying delay, IEEE Trans. Neural Networks 18 (2007) 310-314.
11. C. Li, G. Feng, Delay-interval dependent stability of recurrent neural networks with time-varying delays, Neurocomputing 72 (2009) 1179-1183.
12. Z. Zeng, J. Wang, Improved conditions for global exponential stability of recurrent neural networks with time-varying delays, IEEE Trans. Neural Networks 17 (2006) 623-635.
13. Y. He, G.P. Liu, D. Rees, M. Wu, Stability analysis for neural networks with time-varying interval delay, IEEE Trans. Neural Networks 18 (2007) 1850-1854.
14. Y.-Y. Hou, T.-L. Liao, C.-H. Lien, J.-J. Yan, Stability analysis of neural networks with interval time-varying delays, Chaos 17 (2007) 1-9, (033120).
15. W. Feng, S.X. Yang, W. Fu, H. Wu, Robust stability analysis of uncertain stochastic neural networks with interval time-varying delay, Chaos Solitons Fractals, doi:10.1016/j.chaos.2008.01.024, in press.
16. R. Rakkiyappan, P. Balasubramaniam, S. Lakshmanan, Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays, Phys. Lett. A 372 (2008) 5290-5298.
17. L. Wan, J. Sun, Mean square exponential stability of stochastic delayed Hopfield neural networks, Phys. Lett. A 343 (2005) 306-318.
18. H. Huang, D.W.C. Ho, J. Lam, Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Trans. Circuits Syst. II 52 (2005) 251-255.
19. J. Zhang, P. Shi, J. Qiu, Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays, Nonlinear Anal. Real World Appl. 8 (2007) 1349-1357.
20. H. Huang, G. Feng, Delay dependent stability for uncertain stochastic neural networks with time-varying delay, Physica A 381 (2007) 93-103.
21. W.-H. Chen, X. Lu, Mean square exponential stability of uncertain stochastic delayed neural networks, Phys. Lett. A 372 (2008) 1061-1069.
22. H. Huang, J. Cao, Exponential stability analysis of uncertain stochastic neural networks with multiple delays, Nonlinear Anal. Real World Appl. 8 (2007) 646-653.
23. Z. Wang, Y. Liu, K. Fraser, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays, Phys. Lett. A 354 (2006) 288-297.
24. Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos Solitons Fractals 32 (2007) 62-72.
25. H. Li, B. Chen, Q. Zhou, S. Fang, Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays, Phys. Lett. A 372 (2008) 3385-3394.
26. Y. Liu, Z. Wang, X. Liu, On global exponential stability of generalised stochastic neural networks with mixed time delays, Neurocomputing 70 (2006) 314-326.