Dissipativity analysis of stochastic neural networks with time delays

Nonlinear Dynamics

Volumn 70, Issue 1, 2012, Pages 825-839

  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

Dissipativity analysis; Exponential stability; Neural networks; Stochastic systems; Time delays

Indexed keywords

DELAY PARTITIONING; DISSIPATIVITY; MEAN-SQUARE; NUMERICAL EXAMPLE; STOCHASTIC INTEGRAL; STOCHASTIC NEURAL NETWORK; SUFFICIENT CONDITIONS;

ASYMPTOTIC STABILITY; INTEGRAL EQUATIONS; NEURAL NETWORKS; STOCHASTIC SYSTEMS;

TIME DELAY;

EID: 84867896227     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0499-7     Document Type: Article

References (39)

1. Gupta, M.M.; Jin, L.; Homma, N.: Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory. Wiley-IEEE Press, New York (2003)
2. Chen, H.; Zhu, C.; Hu, P.; Zhang, Y.: Delayed-state-feedback Exponential Stabilization for Uncertain Markovian Jump Systems with Mode-dependent Time-varying State Delays, Nonlinear Dynamics. Nonlinear Dyn. 69, 1023-1039 (2012)
3. Park, J.H.: Design of dynamic output feedback controller for a class of neutral systems with discrete and distributed delays. In: IEE Proceedings Control Theory and Applications, vol. 151, pp. 610-614 (2004)
4. ∞ filtering for stochastic time-delay systems. Int. J. Control. Autom. Syst. 8, 741-747 (2010)
5. Jiang, B.; Du, D.; Cocquempot, V.: Fault detection for discrete-time switched systems with interval time-varying delays. Int. J. Control. Autom. Syst. 9, 396-401 (2011)
6. Xu, L.: Exponential P-stability of singularly perturbed impulsive stochastic delay differential systems. Int. J. Control. Autom. Syst. 9, 966-972 (2011)
7. Zhang, Z.; Zhang, T.; Huang, S.; Xiao, P.: New global exponential stability result to a general Cohen-Grossberg neural networks with multiple delays. Nonlinear Dyn. 67, 2419-2432 (2012)
8. Park, J.H.; Kwon, O.M.; Lee, S.M.: LMI optimization approach on stability for delayed neural networks of neutral-type. Appl. Math. Comput. 196, 236-244 (2008)
9. Li, T.; Wang, T.; Song, A.; Fei, S.: Exponential synchronization for arrays of coupled neural networks with time-delay couplings. Int. J. Control. Autom. Syst. 9, 187-196 (2011)
10. Li, H.; Chen, B.; Zhou, Q.; Qian, W.: Robust stability for uncertain delayed fuzzy Hopfield neural networks with Markovian jumping parameters. IEEE Trans. Syst. Man Cybern.; Part B, Cybern. 39, 94-102 (2009)
11. Faydasicok, O.; Arik, S.: Equilibrium and stability analysis of delayed neural networks under parameter uncertainties. Appl. Comput. Math. 218, 6716-6726 (2012)
12. 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)
13. Tian, J.; Li, Y.; Zhao, J.; Zhong, S.: Delay-dependent stochastic stability criteria for Markovian jumping neural networks with mode-dependent time-varying delays and partially known transition rates. Appl. Comput. Math. 218, 5769-5781 (2012)
14. Wang, Z.; Ho, D.W.C.; Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16, 279-284 (2005)
15. Wang, Z.; Liu, Y.; Liu, X.: State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw. 22, 41-48 (2009)
16. Ahn, C.K.: Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks. Nonlinear Dyn. 61, 483-489 (2010)
17. Li, H.; Gao, H.; Shi, P.: New passivity analysis for neural networks with discrete and distributed delays. IEEE Trans. Neural Netw. 21, 1842-1847 (2011)
18. Li, H.; Lam, J.; Cheung, K.C.: Passivity criteria for continuous-time neural networks with mixed time-varying delays. Appl. Math. Comput. (2012, in press). doi: 10.1016/j.amc.2012.05.002
19. Wu, Z.; Park, J.H.; Su, H.; Chu, J.: New results on exponential passivity of neural networks with time-varying delays. Nonlinear Anal.; Real World Appl. 13, 1593-1599 (2012)
20. Kwon, O.M.; Park, J.H.; Lee, S.M.; Cha, E.J.: A new augmented Lyapunov-Krasovskii functional approach to exponential passivity for neural networks with time-varying delays. Appl. Comput. Math. 217, 10231-10238 (2011)
21. Song, Q.; Cao, J.: Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dyn. 67, 1695-1707 (2012)
22. Mao, X.: Stochastic Differential Equations and Applications. Horwood, Chichester (2007)
23. Blythe, S.; Mao, X.; Liao, X.: Stability of stochastic delay neural networks. J. Franklin Inst. 338, 481-495 (2001)
24. Liao, X.; Mao, X.: Exponential stability and instability of stochastic neural networks. In: Stochastic Analysis and Applications, vol. 14, pp. 165-185 (1996)
25. Yang, R.; Gao, H.; Shi, P.: Novel robust stability criteria for stochastic Hopfield neural networks with time delays. IEEE Trans. Syst. Man Cybern.; Part B, Cybern. 39, 467-474 (2009)
26. 2 performance analysis of stochastic delayed neural networks. IEEE Trans. Neural Netw. 22, 1662-1668 (2011)
27. Lam, J.; Gao, H.; Wang, C.: Stability analysis for continuous systems with two additive time-varying delay components. Syst. Control. Lett. 56, 16-24 (2007)
28. Peaucelle, D.; Arzelier, D.; Henrion, D.; Gouaisbaut, F.: Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation. Automatica 43, 795-804 (2007)
29. Wang, Z.; Liu, Y.; Fraser, K.; Liu, X.: Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354, 288-297 (2006)
30. Wang, Z.; Liu, Y.; Li, M.; Liu, X.: Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 17, 814-820 (2006)
31. Yang, R.; Zhang, Z.; Shi, P.: Exponential stability on stochastic neural networks with discrete interval and distributed delays. IEEE Trans. Neural Netw. 21, 169-175 (2010)
32. Liu, F.; Wu, M.; He, Y.; Yokoyama, R.: Improved delay-dependent stability analysis for uncertain stochastic neural networks with time-varying delay. Neural Comput. Appl. 20, 441-444 (2011)
33. Chen, Y.; Wang, H.; Xue, A.; Lu, R.: Passivity analysis of stochastic time-delay neural networks. Nonlinear Dyn. 61, 71-82 (2010)
34. Brogliato, B.; Lozano, R.; Maschke, B.; Egeland, O.: Dissipative Systems Analysis and Control: Theory and Applications. Springer, London (2007)
35. Feng, Z.; Lam, J.; Gao, H.: α-Dissipativity analysis of singular time-delay systems. Automatica 47, 2548-2552 (2011)
36. Feng, Z.; Lam, J.: Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Trans. Neural Netw. 22, 976-981 (2011)
37. Wu, Z.; Lam, J.; Su, H.; Chu, J.: stability and dissipativity analysis of static neural networks with time delay. IEEE Trans. Neural Netw. Learn. Syst. 23, 199-210 (2012)
38. Shu, Z.; Lam, J.: Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays. Int. J. Control 81, 865-882 (2008)
39. Park, P.G.; Ko, J.W.; Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47, 235-238 (2011)