Modified criteria for global robust stability of interval delayed neural networks

Applied Mathematics and Computation

Volumn 215, Issue 8, 2009, Pages 3124-3133

  Singh, Vimal ^a  

^a ATILIM UNIVERSITY   (Turkey)

Author keywords

Dynamical interval neural networks; Equilibrium analysis; Global robust stability; Hopfield neural networks; Neural networks; Nonlinear systems; Time delay systems

Indexed keywords

DYNAMICAL INTERVAL NEURAL NETWORKS; EQUILIBRIUM ANALYSIS; GLOBAL ROBUST STABILITY; INTERVAL DELAYED NEURAL NETWORKS; INTERVAL NEURAL NETWORK; NUMERICAL SIMULATION; TIME-DELAY SYSTEMS;

COMPUTER SIMULATION; DELAY CONTROL SYSTEMS; NEURAL NETWORKS; NONLINEAR SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; SYSTEM STABILITY; TIME DELAY;

HOPFIELD NEURAL NETWORKS;

EID: 70449525124     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.10.006     Document Type: Article

References (78)

1. Zhang Q., Ma R., Wang C., and Xu J. On the global stability of delayed neural networks. IEEE Trans. Automat. Contr. 48 5 (2003) 794-797
2. Arik S. Global asymptotic stability of a larger class of neural networks with constant time delays. Phys. Lett. A 311 6 (2003) 504-511
3. Lu W., Rong L., and Chen T. Global convergence of delayed neural network systems. Int. J. Neural Syst. 13 3 (2003) 193-204
4. Zhang Q., Wei X., and Xu J. Global asymptotic stability of Hopfield neural networks with transmission delays. Phys. Lett. A 318 4-5 (2003) 399-405
5. Qi H.-D., and Qi L. Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis. IEEE Trans. Neural Networks 15 1 (2004) 99-109
6. Cao J., and Chen T. Globally exponentially robust stability and periodicity of delayed neural networks. Chaos, Solitons Fractals 22 4 (2004) 957-963
7. Singh V. A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Networks 15 1 (2004) 223-225
8. Singh V. Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proc. Contr. Theory Appl. 151 1 (2004) 125-129
9. Li Y.K. Existence and stability of periodic solution for BAM neural networks with distributed delays. Appl. Math. Comput. 159 3 (2004) 847-862
10. Wang L. Stability of Cohen-Grossberg neural networks with distributed delays. Appl. Math. Comput. 160 1 (2005) 93-110
11. Zhang Q., Wei X.P., and Xu J. On global exponential stability of delayed cellular neural networks with time-varying delays. Appl. Math. Comput. 162 2 (2005) 679-686
12. Yang X.F., Li C.D., Liao X.F., Evans D.J., and Megson G.M. Global exponential periodicity of a class of bidirectional associative memory networks with finite distributed delays. Appl. Math. Comput. 171 1 (2005) 108-121
13. Sun C., and Feng C.B. Global robust exponential stability of interval neural networks with delays. Neural Process. Lett. 17 (2005) 107-115
14. Xu S.Y., Lam J., Ho D.W.C., and Zou Y. Delay-dependent exponential stability for a class of neural networks with time delays. J. Comput. Appl. Math. 183 1 (2005) 16-28
15. Xu S., Lam J., Ho D.W.C., and Zou Y. Improved global robust asymptotic stability criteria for delayed cellular neural networks. IEEE Trans. Syst. Man Cybern. B 35 6 (2005) 1317-1321
16. Lu H.T. Comments on 'A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks'. IEEE Trans. Neural Networks 16 3 (2005) 778-779
17. Qi H.-D., and Qi L. Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis II. IEEE Trans. Neural Networks 16 6 (2005) 1701-1706
18. Jiang M.H., Shen Y., and Liao X.X. Boundedness and global exponential stability for generalized Cohen-Grossberg neural networks with variable delay. Appl. Math. Comput. 172 1 (2006) 379-393
19. Yang Z.C., and Xu D.Y. Impulsive effects on stability of Cohen-Grossberg neural networks with variable de-lays. Appl. Math. Comput. 177 1 (2006) 63-78
20. Wu C., Ruan J., and Lin W. On the existence and stability of the periodic solution in the Cohen-Grossberg neural network with time delay and high-order terms. Appl. Math. Comput. 177 1 (2006) 194-210
21. Yan X.-P., and Li W.-T. Hopf bifurcation and global periodic solutions in a delayed predator-prey system. Appl. Math. Comput. 177 1 (2006) 427-445
22. Zhu W., Xu D.Y., and Yang Z.C. Global exponential stability of impulsive delay difference equation. Appl. Math. Comput. 181 1 (2006) 65-72
23. Park J.H. A new stability analysis of delayed cellular neural networks. Appl. Math. Comput. 181 1 (2006) 200-205
24. Jiang M.H., Shen Y., and Liao X.X. Global stability of periodic solution for bidirectional associative memory neural networks with varying-time delay. Appl. Math. Comput. 182 1 (2006) 509-520
25. Park J.H. Global exponential stability of cellular neural networks with variable delays. Appl. Math. Comput. 183 2 (2006) 1214-1219
26. Cheng C.-J., Liao T.-L., Yan J.-J., and Hwang C.-C. Globally asymptotic stability of a class of neutral-type ne-ural networks with delays. IEEE Trans. Syst. Man Cybern. B 36 5 (2006) 1191-1195
27. Yuan K., Cao J., and Li H.-X. Robust stability of switched Cohen-Grossberg neural networks with mixed time-varying delays. IEEE Trans. Syst. Man Cybern. 36 6 (2006) 1356-1363
28. He Y., Wu M., and She J.H. An improved global asymptotic stability criterion for delayed cellular neural networks. IEEE Trans. Neural Networks 17 1 (2006) 250-252
29. Zeng Z.G., and Wang J. Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans. Neural Networks 17 3 (2006) 623-635
30. Cao J.D., Yuan K., and Li H.X. Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Networks 17 6 (2006) 1646-1651
31. Yu W.W., and Yao L.L. Global robust stability of neural networks with time varying delays. J. Comput. Appl. Math. 206 2 (2007) 679-687
32. Park J.H. Further note on global exponential stability of uncertain cellular neural networks with variable delays. Appl. Math. Comput. 188 1 (2007) 850-854
33. Cao J.W., Zhong S.M., and Hu Y.Y. Global stability analysis for a class of neural networks with varying delays and control input. Appl. Math. Comput. 189 2 (2007) 1480-1490
34. Wang Q., and Liu X.Z. Exponential stability of impulsive cellular neural networks with time delay via Lyapunov functionals. Appl. Math. Comput. 194 1 (2007) 186-198
35. He Y., Liu G.P., and Rees D. New delay-dependent stability criteria for neural networks with time-varying de-lay. IEEE Trans. Neural Networks 18 1 (2007) 310-314
36. Liao X., and Yu J. Robust stability for interval Hopfield neural networks with time delay. IEEE Trans. Neural Networks 9 5 (1998) 1042-1046
37. Liao X., Wong K., Wu Z., and Chen G. Novel robust stability for interval-delayed Hopfield neural networks. IEEE Trans. Circuits Syst. I 48 11 (2001) 1355-1359
38. Arik S. Global robust stability of delayed neural networks. IEEE Trans. Circuits Syst. I 50 1 (2003) 156-160
39. Singh V. Global robust stability of delayed neural networks: an LMI approach. IEEE Trans. Circuits Syst. II 52 1 (2005) 33-36
40. Cao J., Huang D.-S., and Qu Y. Global robust stability of delayed recurrent neural networks. Chaos, Solitons Fractals 23 1 (2005) 221-229
41. Cao J., and Wang J. "Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I 52 2 (2005) 417-426
42. Ozcan N., and Arik S. Global robust stability analysis of neural networks with multiple time delays. IEEE Trans. Circuits Syst. I 53 1 (2006) 166-176
43. Singh V. Improved global robust stability criterion for delayed neural networks. Chaos, Solitons Fractals 31 1 (2007) 224-229
44. Singh V. On global robust stability of interval Hopfield neural networks with delay. Chaos, Solitons Fractals 33 4 (2007) 1183-1188
45. Qi H. New sufficient conditions for global robust stability of delayed neural networks. IEEE Trans. Circuits Syst. I 54 5 (2007) 1131-1141
46. Shen T., and Zhang Y. Improved global robust stability criteria for delayed neural networks. IEEE Trans. Circuits Syst. II 54 8 (2007) 715-719
47. Zhang H., Wang Z., and Liu D. Robust exponential stability of recurrent neural networks with multiple time-varying delays. IEEE Trans. Circuits Syst. II 54 8 (2007) 730-734
48. Li C., and Liao X. Global robust stability criteria for interval delayed neural networks via an LMI approach. IEEE Trans. Circuits Syst. II 53 9 (2006) 901-905
49. Singh V. A new criterion for global robust stability of interval delayed neural networks. J. Comput. Appl. Math. 221 1 (2008) 219-225
50. Zhou L., and Hu G. Global exponential periodicity and stability of cellular neural networks with variable and distributed delays. Appl. Math. Comput. 195 2 (2008) 402-411
51. Wang B., Zhong S., and Liu X. Asymptotical stability criterion on neural networks with multiple time-vary-varying delays. Appl. Math. Comput. 195 2 (2008) 809-818
52. Park J.H., Kwon O.M., and Lee S.M. LMI optimization approach on stability for delayed neural networks of neutral-type. Appl. Math. Comput. 196 1 (2008) 236-244
53. Cao J.W., Zhong S.M., and Hu Y.Y. Novel delay-dependent stability conditions for a class of MIMO networked control systems with nonlinear perturbation. Appl. Math. Comput. 197 2 (2008) 797-809
54. Singh V. Improved global robust stability for interval-delayed Hopfield neural networks. Neural Process. Lett. 27 3 (2008) 257-265
55. Zhou Q., and Wan L. Exponential stability of stochastic delayed Hopfield neural networks. Appl. Math. Comput. 199 1 (2008) 84-89
56. Kwon O.M., and Park J.H. On improved delay-dependent stability criterion of certain neutral differential equations. Appl. Math. Comput. 199 1 (2008) 385-391
57. Park J.H., and Kwon O.M. On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays. Appl. Math. Comput. 199 2 (2008) 435-446
58. Park J.H., Park C.H., Kwon O.M., and Lee S.M. A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl. Math. Comput. 199 2 (2008) 716-722
59. Meng Y., Guo S., and Huang L. Convergence dynamics of Cohen-Grossberg neural networks with continuously distributed delays. Appl. Math. Comput. 202 1 (2008) 188-199
60. Park J.H., and Kwon O.M. Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202 1 (2008) 360-369
61. Nam P.T. An improved criterion for exponential stability of linear systems with multiple time delays. Appl. Math. Comput. 202 2 (2008) 870-876
62. Bai C. Global stability of almost periodic solutions of Hopfield neural networks with neutral time-vary-ing delays. Appl. Math. Comput. 203 1 (2008) 72-79
63. Park J.H., Kwon O.M., and Lee S.M. State estimation for neural networks of neutral-type with interval time-varying delays. Appl. Math. Comput. 203 1 (2008) 217-223
64. Kwon O.M., and Park J.H. New delay-dependent robust stability criterion for uncertain neural networks with time-varying delays. Appl. Math. Comput. 205 1 (2008) 417-427
65. Kwon O.M., Park J.H., and Lee S.M. On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays. Appl. Math. Comput. 203 2 (2008) 843-853
66. Kwon O.M., and Park J.H. Exponential stability analysis for uncertain cellular neural networks with discrete and distributed time-varying delays. Appl. Math. Comput. 212 2 (2009) 530-541
67. Kwon O.M., Park J.H., and Lee S.M. On robust stability criterion for dynamic systems with time-varying de-delays and nonlinear perturbations. Appl. Math. Comput. 203 3 (2008) 937-942
68. Zhu W. Global exponential stability of impulsive reaction-diffusion equation with variable delays. Appl. Math. Comput. 205 1 (2008) 362-369
69. Yu J., Zhang K., Fei S., and Li T. Simplified exponential stability analysis for recurrent neural networks with discrete and distributed time-varying delays. Appl. Math. Comput. 205 1 (2008) 465-474
70. Singh V. Improved global robust stability of interval delayed neural networks via split interval: generalizations. Appl. Math. Comput. 206 1 (2008) 290-297
71. Guo Y. Mean square global asymptotic stability of stochastic recurrent neural networks with distributed delays. Appl. Math. Comput. 215 2 (2009) 791-795
72. Zhang Y., Yue D., and Tian E. New stability criteria of neural networks with interval time-varying delay: a piecewise delay method. Appl. Math. Comput. 208 1 (2009) 249-259
73. Park J.H., and Kwon O.M. Further results on state estimation for neural networks of neutral-type with time-varying delay. Appl. Math. Comput. 208 1 (2009) 69-75
74. Samli R., and Arik S. New results for global stability of a class of neutral-type neural systems with time delays. Appl. Math. Comput. 210 2 (2009) 564-570
75. Park J.H. Robust stability of bidirectional associative memory neural networks with time delays. Phys. Lett. A 349 6 (2006) 494-499
76. Park J.H. A novel criterion for global asymptotic stability of BAM neural networks with time delays. Chaos, Solitons, Fractals 29 2 (2006) 446-453
77. Park J.H. An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays. Chaos, Solitons, Fractals 32 2 (2007) 800-807
78. Kwon O.M., Park J.H., and Lee S.M. Augmented Lyapunov functional approach to stability of uncertain neural systems with time-varying delays. Appl. Math. Comput. 207 1 (2009) 202-212