Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

Nonlinear Dynamics

Volumn 66, Issue 4, 2011, Pages 479-487

  Wu, Huaiqin ^a   Tao, Feng ^a   Qin, Leijie ^a   Shi, Rui ^a   He, Lijun ^a  

^a YANSHAN UNIVERSITY   (China)

Author keywords

Brouwer degree; Global robust stability; Inverse H lder activation functions; Linear matrix inequality; Neural networks

Indexed keywords

ACTIVATION FUNCTIONS; BROUWER DEGREE; EQUILIBRIUM POINT; EXISTENCE AND UNIQUENESS; EXPONENTIALLY STABLE; GLOBAL ROBUST EXPONENTIAL STABILITIES; GLOBAL ROBUST STABILITY; INTERVAL NEURAL NETWORK; LINEAR MATRIX INEQUALITY TECHNIQUES; LYAPUNOV FUNCTIONALS; NEURON ACTIVATION FUNCTION; NUMERICAL EXAMPLE; ROBUST EXPONENTIAL STABILITY; SUFFICIENT CONDITIONS; THEORETICAL RESULT;

HOLMIUM; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; ROBUSTNESS (CONTROL SYSTEMS);

NEURAL NETWORKS;

EID: 82255183314     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9926-9     Document Type: Article

References (38)

1. V. Singh 2008 A new criterion for global robust stability of interval delayed neural networks J. Comput. Appl. Math. 221 219 225 2458765 1162.34352 10.1016/j.cam.2007.10.059
2. V. Singh 2008 Improved global robust stability of interval delayed neural networks via split interval: generalizations Appl. Math. Comput. 206 290 297 2474974 1168.34357 10.1016/j.amc.2008.08.036
3. V. Singh 2008 Improved global robust stability for interval-delayed Hopfield neural networks Neural Process. Lett. 27 257 265 10.1007/s11063-008- 9074-0
4. V. Singh 2010 New LMI-based criteria for global robust stability of delayed neural networks Appl. Math. Model. 10.1016/j.apm.2010.01.005
5. R. Gau C. Lien J. Hsieh 2007 Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach Chaos Solitons Fractals 32 1258 1267 2286294 1134.34049 10.1016/j.chaos.2005.11. 036 (Pubitemid 44909750)
6. T. Li L. Guo C. Sun 2007 Robust stability for neural networks with time-varying delays and linear fractional uncertainties Neurocomputing 71 421 427 10.1016/j.neucom.2007.08.012 (Pubitemid 350028674)
7. O. Ou 2007 Global robust exponential stability of delayed neural networks: an LMI approach Chaos Solitons Fractals 32 1742 1748 2299089 1160.34345 10.1016/j.chaos.2005.12.026 (Pubitemid 46136965)
8. H. Qi 2007 New sufficient conditions for global robust stability of delayed neural networks IEEE Trans. Circuits Syst. I 54 1131 1141 10.1109/TCSI.2007.895524 (Pubitemid 46773782)
9. J. Qiu H. Yang J. Zhang Z. Gao 2009 New robust stability criteria for uncertain neural networks with interval time-varying delays Chaos Solitons Fractals 39 579 585 2518912 1197.34141 10.1016/j.chaos.2007.01.087
10. J. Qiu J. Zhang J. Wang Y. Xia P. Shi 2008 A new global robust stability criteria for uncertain neural networks with fast time-varying delays Chaos Solitons Fractals 37 360 368 2402631 1141.93046 10.1016/j.chaos.2007.10.040 (Pubitemid 351380492)
11. T. Shen Y. Zhang 2007 Improved global robust stability criteria for delayed neural networks IEEE Trans. Circuits Syst. II 54 715 759 2460427 10.1109/TCSII.2007.898467 (Pubitemid 47250013)
12. Z. Wang H. Zhang W. Yu 2007 Robust exponential stability analysis of neural networks with multiple time delays Neurocomputing 70 2534 2543 10.1016/j.neucom.2006.07.014 (Pubitemid 46825355)
13. Z. Wang H. Zhang W. Yu 2009 Robust stability of Cohen-Grossberg neural networks via state transmission matrix IEEE Trans. Neural Netw. 20 169 174 10.1109/TNN.2008.2009119
14. Z. Wang H. Zhang W. Yu 2009 Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay Neurocomputing 72 1105 1110 10.1016/j.neucom.2008.03.001
15. W. Wu B. Cui 2008 Global robust exponential stability of delayed neural networks Chaos Solitons Fractals 35 747 754 2379370 1138.93332 10.1016/j.chaos.2006.05.096 (Pubitemid 47484435)
16. W. Yu L. Yao 2007 Global robust stability of neural networks with time varying delays J. Comput. Appl. Math. 206 679 687 2333705 1115.37017 10.1016/j.cam.2006.08.017 (Pubitemid 46856033)
17. B. Zhang S. Xu Y. Li 2007 Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays Int. J. Neural Syst. 17 207 218 1138.60331 10.1142/S012906570700107X (Pubitemid 47117611)
18. H. Zhang Z. Wang D. Liu 2008 Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time-varying delays IEEE Trans. Neural Netw. 19 1942 1955 10.1109/TNN.2008.2006337
19. H. Zhang Z. Wang D. Liu 2007 Robust exponential stability of cellular neural networks with multiple time varying delays IEEE Trans. Circuits Syst. II 54 730 734 2460427 10.1109/TCSII.2007.896799 (Pubitemid 47250016)
20. G. Wang J. Cao 2009 Robust exponential stability analysis for stochastic genetic networks with uncertain parameters Commun. Nonlinear Sci. Numer. Simul. 14 3369 3378 2502407 1221.93217 10.1016/j.cnsns.2009.01.004
21. O. Kwon J. Park S. Lee 2008 On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays Appl. Math. Comput. 197 864 873 2400710 1144.34052 10.1016/j.amc.2007.08.048 (Pubitemid 351284570)
22. O. Kwon J. Park S. Lee 2008 On roust stability for uncertain neural networks with interval time-varying delays IET Control Theory Appl. 2 625 634 2436160 10.1049/iet-cta:20070325
23. S. Senan S. Arik 2009 New results for global robust stability of bidirectional associative memory neural networks with multiple time delays Chaos Solitons Fractals 41 2106 2114 2537790 1198.34163 10.1016/j.chaos.2008.08.010
24. W. Su Y. Chen 2009 Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays Commun. Nonlinear Sci. Numer. Simul. 14 2293 2300 2474475 1221.93215 10.1016/j.cnsns.2008.05.001
25. L. Wang Y. Zhang Z. Zhang Y. Wang 2009 LMI-based approach for global exponential robust stability for reaction-diffusion uncertain neural networks with time-varying delay Chaos Solitons Fractals 41 900 905 2535623 1198.93168 10.1016/j.chaos.2008.04.020
26. J. Shao T. Huang S. Zhou 2009 An analysis on global robust exponential stability of neural networks with time-varying delays Neurocomputing 72 1993 1998 10.1016/j.neucom.2008.11.023
27. R. Zhang L. Wang 2009 Global exponential robust stability of interval cellular neural networks with S-type distributed delays Math. Comput. Model. 50 380 385 1185.34110 10.1016/j.mcm.2009.04.016
28. W. Zhao Q. Zhu 2010 New results of global robust exponential stability of neural networks with delays Nonlinear Anal. Real World Appl. 11 1190 1197 2571289 1196.34098 10.1016/j.nonrwa.2009.01.008
29. C. Zheng H. Zhang Z. Wang 2009 Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties Neurocomputing 72 1744 1754 10.1016/j.neucom.2008.08. 017
30. C. Zheng X. Jing Z. Wang J. Feng 2009 Further results for robust stability of cellular neural networks with linear fractional uncertainty Commun. Nonlinear Sci. Numer. Simul. 10.1016/j.cnsns.2009.11.007
31. L. Sheng H. Yang 2009 Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays Chaos Solitons Fractals 40 2102 2113 2533207 1198.93165 10.1016/j.chaos.2007.09.098
32. L. Sheng H. Yang 2009 Robust stability of uncertain Markovian jumping Cohen-Grossberg neural networks with mixed time-varying delays Chaos Solitons Fractals 42 2120 2128 2559878 1198.93166 10.1016/j.chaos.2009.03.161
33. J. Zhang S. Peng J. Qiu 2008 Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties Chaos Solitons Fractals 38 1 160 167 2417651 10.1016/j.chaos.2006.10.068 (Pubitemid 351503978)
34. Y. Chen A. Xue R. Lu S. Zhou 2008 On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations Nonlinear Anal. 68 2464 2470 2398664 1147.34352 10.1016/j.na.2007.01.070 (Pubitemid 351295829)
35. H. Wu X. Xue 2008 Stability analysis for neural networks with inverse Lipschizan neuron activations and impulses Appl. Math. Model. 32 2347 2359 2439705 1156.34333 10.1016/j.apm.2007.09.002
36. H. Wu 2009 Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations Nonlinear Anal.; Real World Appl. 10 2297 2306 2508439 1163.92308 10.1016/j.nonrwa.2008.04.016
37. Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985)
38. Miller, P.; Michel, A.: Differential Equations. Academic Press, San Diego (1982)