Delay-Dependent Exponential Synchronization Criteria for Chaotic Neural Networks with Time-Varying Delays

Brazilian Journal of Physics

Volumn 42, Issue 3-4, 2012, Pages 207-218

  Jeeva Sathya Theesar, S ^a   Chandran, R ^a,b   Balasubramaniam, P ^a,c  

^a GANDHIGRAM RURAL UNIVERSITY   (India)

^b Government Arts College   (India)

^c UNIVERSITY OF MALAYA   (Malaysia)

Author keywords

Delay decomposition; Delayed neural networks; Exponential synchronization; Maximum admissible upper bound (MAUB); Time varying delay

Indexed keywords

EID: 84862660907     PISSN: 01039733     EISSN: 16784448     Source Type: Journal    
DOI: 10.1007/s13538-012-0070-5     Document Type: Article

References (24)

1. T. Carroll, L. Pecora, Synchronizing chaotic circuits. Phys. Rev. Lett. 64, 821-24 (1990).
2. T. Carroll, L. Pecora, Synchronization in chaotic system. IEEE Trans. Circuits Syst. Part I 38, 453-56 (1991).
3. H. Yu, Y. Liu, Chaotic synchronization based on stability creterion of linear systems. Phys. Lett. A 314, 292-298 (2003).
4. M. Feki, An adaptive chaos synchronization scheme applied to secure communication. Chaos Solitons Fractals 18, 141-148 (2003).
5. J. J. Hopfield, Neural networks and physical systyems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79, 2554-2558 (1982).
6. L. O. Chua, L. Yang, Cellular neural networks: theory. IEEE Trans. Circuits Syst. Part I 35, 1257-1272 (1988).
7. X. Y. Lou, B. T. Cui, New LMI conditions for delay-dependent asymptotic stability of Hopfield neural networks. Neurocomputing 69, 2374-78 (2006).
8. X. Zhang, Q-L Han, New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks. IEEE Trans. Neural Netw. 20, 533-539 (2009).
9. C. Zheng, H. Zhang, Z. Wang, New delay-dependent global exponential stability criterion for cellular-type neural networks with time-varying delays. IEEE Trans. Circuits Syst. Part II 56, 250-254 (2009).
10. X. Zhang, Q. Han, Global asymptotic stability for a class of generalized neural networks with interval time-varying delays. IEEE Trans. Neural Netw. 22, 1180-1192 (2011).
11. P. Balasubramaniam, R. Chandran, Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time varying delay. Commun. Nonlinear Sci. Numer. Simul. 16, 2098-2108 (2011).
12. P. Balasubramaniam, S. Lakshmanan, S. Jeeva Sathya Theesar, State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60, 661-675 (2010).
13. H. Huang, G. Feng, J. Cao, An LMI approach to delay-dependent state estimation for delayed neural networks. Neurocomputing 71, 2857-2867 (2008).
14. J. Hu, Synchronization conditions for chaotic nonlinear continuous neural networks. Chaos Solitons Fractals 41, 2495-2501 (2009).
15. G. Chen, J. Zhou, Z. liu, Global synchronization of coupled delayed neural networks with application to chaotic CNN models. Int. J. Bifur. Chaos 14, 2229-40 (2004).
16. Chao Jung Ch, The-Luliao, Jun-JuthYan, Chi-chuan Hwang, Exponential synchronization of a class of neural networks with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B. 36, 209-215 (2006).
17. B. Cui, X. Lou, Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fractals 39, 288-294 (2009).
18. L. Wang, W. Ding, D. Chen, Synchronization schemes of a class of fuzzy cellular neural networks based on adaptive control. Phys. Lett. A 374, 1440-449 (2010).
19. X. Gao, S. Zhong, F. Gao, Exponential synchronization of neural networks with time-varying delays. Nonlinear Anal. 71, 2003-2011 (2009).
20. P. Balasubramaniam, R. Chandran, S. Jeeva Sathya Theesar, Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn. Neurodyn. 5, 361-371 (2011).
21. X. M. Zhang, Q-L. Han, A delay decomposition approach to delay dependent stability for linear systems with time varying delays. Int. J. Robust Nonlinear Control 19, 1922-1930 (2009).
22. Q-L. Han, A delay decomposition approach to stability and H∞ control of linear time-delay systems-part II: H∞ control, in Proceedings of the 7th World Congress on Intelligent Control and Automation (Chongqing, China, 25-27 June 2008).
23. S. Boyd et al., Linear Matrix Inequalities in Systems and Control Theory (SIAM, Philadelphia, 1994).
24. H. K. Khalil, Nonlinear Systems (Macmillan, New York, 1992).