Discontinuous lyapunov functional approach to synchronization of time-delay neural networks using sampled-data

Nonlinear Dynamics

Volumn 69, Issue 4, 2012, Pages 2021-2030

  Wu, Zheng Guang ^a,b   Park, Ju H ^a   Su, Hongye ^b   Chu, Jian ^b  

^a Yeungnam University   (South Korea)

^b STATE KEY LABORATORY OF INDUSTRIAL CONTROL TECHNOLOGY   (China)

Author keywords

Neural networks; Sampled data control; Synchronization; Time delay

Indexed keywords

CONSERVATIVE SYNCHRONIZATION; DESIGN METHOD; INPUT DELAYS; LINEAR MATRIX INEQUALITY APPROACH; LYAPUNOV FUNCTIONALS; MASTER SYSTEMS; NUMERICAL EXAMPLE; SAMPLED-DATA; SAMPLED-DATA CONTROL; SAMPLED-DATA CONTROLLER; SAW-TOOTH STRUCTURE; SLAVE SYSTEMS; SYNCHRONIZATION PROBLEM; TIME DELAY NEURAL NETWORKS; TIME-VARYING DELAY;

DELAY CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; TIME DELAY;

SYNCHRONIZATION;

EID: 84866126761     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0404-4     Document Type: Article

References (48)

1. Zhang, H., Ma, T., Huang, G., Wang, Z.: Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40, 831-844 (2010
2. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990
3. Cao, J., Li, H., Ho, D.W.C.: Synchronization criteria of Lur'e systems with time-delay feedback control. Chaos Solitons Fractals 23, 1285-1298 (2005
4. Xiong,W., Xie,W., Cao, J.: Adaptive exponential synchronization of delayed chaotic networks. Physica A 370, 832-842 (2006 (Pubitemid 44310863)
5. Karimi, H.R.: Robust synchronization and fault detection of uncertain master-slave systems with mixed time-varying delays and nonlinear perturbations. Int. J. Control. Autom. Syst. 9, 671-680 (2011
6. Li, T., Wang, T., Song, A., Fei, S.: Exponential synchronization for arrays of coupled neural networks with timedelay couplings. Int. J. Control. Autom. Syst. 9, 187-196 (2011
7. Lee, S.M., Kwon, O.M., Park, J.H.: Regional asymptotic stability analysis for discrete-time delayed systems with saturation nonlinearity. Nonlinear Dyn. 67, 885-892 (2012
8. Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval timevarying delay feedback control. Nonlinear Dyn. 63, 239-252 (2011
9. Lee, S.M., Choi, S.J., Ji, D.H., Park, J.H., Won, S.C.: Synchronization for chaotic Lur'e systems with sector restricted nonlinearities via delayed feedback control. Nonlinear Dyn. 59, 277-288 (2010
10. Han, Q.L.: On designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 54, 1573-1583 (2007
11. Lee, S.M., Ji, D.H., Park, J.H., Won, S.C.: H8 synchronization of chaotic systems via dynamic feedback approach. Phys. Lett. A 372, 4905-4912 (2008
12. Huang, H., Feng, G., Cao, J.: Exponential synchronization of chaotic Lur'e systems with delayed feedback control. Nonlinear Dyn. 57, 441-453 (2009
13. Miao, Q., Tang, Y., Lu, S., Fang, J.: Lag synchronization of a class of chaotic systems with unknown parameters. Nonlinear Dyn. 57, 107-112 (2009
14. Zhang, J., Tang,W.: Control and synchronization for a class of new chaotic systems via linear feedback. Nonlinear Dyn. 58, 675-686 (2009
15. Park, J.H., Kwon, O.M.: Synchronization of cellular neural networks of neutral type via dynamic feedback controller. Chaos Solitons Fractals 42, 1299-1304 (2009
16. Zhang, H., Huang, W., Wang, Z., Chai, T.: Adaptive synchronization between two different chaotic systems with unknown parameters. Phys. Lett. A 350, 363-366 (2006 (Pubitemid 43129366)
17. Zhang, C., He, Y., Wu, M.: Improved global asymptotical synchronization of chaotic Lur'e systems with sampleddata control. IEEE Trans. Circuits Syst. II, Express Briefs 56, 320-324 (2009
18. Li, P., Cao, J., Wang, Z.: Robust impulsive synchronization of coupled delayed neural networks with uncertainties. Physica A 373, 261-272 (2007 (Pubitemid 44647697)
19. Lu, J., Cao, J., Ho, D.W.C.: Adaptive stabilization and synchronization for chaotic Lur'e systems with time-varying delay. IEEE Trans. Circuits Syst. I, Regul. Pap. 55, 1347-1356 (2008
20. Balasubramaniam, P., Chandran, R., Theesar, S.J.S.: Synchronization of chaotic nonlinear continuous neural networks with time-varying delay. Cogn. Neurodyn. 5, 361-371 (2011
21. Gupta, M.M., Jin, L., Homma, N.: Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. Wiley/IEEE Press, New York (2003
22. Wang, Z., Zhang, H.: Global asymptotic stability of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays. IEEE Trans. Neural Netw. 20, 39-49 (2010
23. Kwon, O.M., Park, J.H., Lee, S.M.: Augmented Lyapunov functional approach to stability of uncertain neutral systems with time-varying delays. Appl. Math. Comput. 207, 202-212 (2009
24. Park, J.H., Kwon, O.M.: Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl. Math. Comput. 208, 69-75 (2009
25. Park, M.J., Kwon, O.M., Park, J.H., Lee, S.M.: A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays. Appl. Math. Comput. 217, 7197-7209 (2011
26. Ji, D., Koo, J.H., Won, S.C., Lee, S.M., Park, J.H.: Passivity-based control for Hopfield neural networks using convex representation. Appl. Math. Comput. 217, 6168-6175 (2011
27. Kwon, O.M., Lee, S., Park, J.H.: Improved delaydependent exponential stability for uncertain stochastic neural networks with time-varying delays. Phys. Lett. A 374, 1232-1241 (2010
28. He, Y., Liu, G., Rees, D.: New delay-dependent stability criteria for neural networks with time-varying delay. IEEE Trans. Neural Netw. 18, 310-314 (2007 (Pubitemid 46062938)
29. Wu, L., Feng, Z., Zheng, W.: Exponential stability analysis for delayed neural networks with switching parameters: Average dwell time approach. IEEE Trans. Neural Netw. 21, 1396-1407 (2010
30. Liu, Y.,Wang, Z., Serrano, A., Liu, X.: Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis. Phys. Lett. A 362, 480-488 (2007
31. Xu, S., Lam, J., Ho, D.W.C., Zou, Y.: Improved global robust asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 35, 1317-1321 (2005 (Pubitemid 41800430)
32. Zhang, H., Liu, Z., Huang, G., Wang, Z.: Novel weightingdelay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans. Neural Netw. 21, 91-106 (2010
33. Balasubramaniam, P., Lakshmanan, S., Theesar, S.J.S.: State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60, 661-675 (2010
34. Feng, Z., Lam, J.: Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Trans. Neural Netw. 22, 976-981 (2011
35. Liu, X., Chen, T., Cao, J., Lu, W.: Dissipativity and quasisynchronization for neural networks with discontinuous activations and parameter mismatches. Neural Netw. 24, 1013-1021 (2011
36. Liu, X., Cao, J.: Local synchronization of one-to-one coupled neural networks with discontinuous activations. Cogn. Neurodyn. 5, 13-20 (2011
37. Yu, W., Cao, J.: Synchronization control of stochastic delayed neural networks. Physica A 373, 252-260 (2007 (Pubitemid 44647680)
38. Karimi, H.R., Maass, P.: Delay-range-dependent exponential H8 synchronization of a class of delayed neural networks. Chaos Solitons Fractals 41, 1125-1135 (2009
39. Qi, D., Liu, M., Qiu, M., Zhang, S.: Exponential H8 synchronization of general discrete-time chaotic neural networks with or without time delays. IEEE Trans. Neural Netw. 21, 1358-1365 (2010
40. Zhang, C., He, Y., Wu, M.: Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing 74, 265-273 (2010
41. Liu, K., Fridman, E.:Wirtinger's inequality and Lyapunovbased sampled-data stabilization. Automatica 48, 102-108 (2012
42. Gao, H., Chen, T., Lam, J.: A new delay system approach to network-based control. Automatica 44, 39-52 (2008
43. Wang, Y., Zhang, H., Wang, X., Yang, D.: Networked synchronization control of coupled dynamic networks with time-varying delay. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40, 1468-1479 (2010
44. Yue, D., Han, Q., Lam, J.: Network-based robust H8 control of systems with uncertainty. Automatica 41, 999-1007 (2005 (Pubitemid 40556809)
45. Liu, Y., Wang, Z., Liu, X.: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19, 667-675 (2006
46. Gu, K., Kharitonov, V.K., Chen, J.: Stability of Time-Delay Systems. Birkhäuser, Boston (2003
47. Liu, K., Suplin, V., Fridman, E.: Stability of linear systems with general sawtooth delay. IMA J. Math. Control Inf. 27, 419-436 (2011
48. Wang, Z., Liu, Y., Yu, L., Liu, X.: Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356, 346-352 (2006) (Pubitemid 43947472)