Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays

Neurocomputing

Volumn 73, Issue 7-9, 2010, Pages 1265-1271

  Wu, Xiru ^a   Wang, Yaonan ^a   Huang, Lihong ^a   Zuo, Yi ^b,c  

^a HUNAN UNIVERSITY   (China)

^b CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c UNIVERSITY OF GUELPH   (Canada)

Author keywords

Delayed neural networks; Discontinuous activation functions; Global robust exponential stability; LMIs; Norm bounded uncertainties

Indexed keywords

ACTIVATION FUNCTIONS; DELAYED NEURAL NETWORKS; GLOBAL ROBUST EXPONENTIAL STABILITIES; LYAPUNOV-KRASOVSKII STABILITY THEORY; NORM-BOUNDED UNCERTAINTY; NUMERICAL EXAMPLE; ROBUST EXPONENTIAL STABILITY; TIME-VARYING DELAY; TIME-VARYING DELAYED; UNCERTAIN NEURAL NETWORKS;

ASYMPTOTIC STABILITY; EXPONENTIAL FUNCTIONS; LINEAR MATRIX INEQUALITIES; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS; UNCERTAIN SYSTEMS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CRITERION VARIABLE; LINEAR MATRIX INEQUALITY; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; PROCESS CONTROL; STATISTICAL CONCEPTS; TIME DELAY SYSTEM; UNCERTAINTY; VALIDATION PROCESS;

EID: 77649233055     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2010.01.002     Document Type: Article

References (36)

1. Zhang Q., Wei X., and Xu J. A new global stability result for delayed neural networks. Nonlin. Anal. Real World Appl. 8 (2007) 1024-1028
2. Li C., and Liao X. Global robust stability criteria for interval delayed neural networks via an LMI approach. IEEE Trans. Circuits Syst. II Express Briefs 53 (2006) 901-905
3. Li H., et al. Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372 (2008) 3385-3394
4. Qi H. New sufficient conditions for global robust stability of delayed neural networks. IEEE Trans. Circuits Syst. I Regular Papers 18 (2006) 683-708
5. Li C., Liao X., and Zhang R. A global exponential robust stability criterion for interval delayed neural networks with variable delays. Neurocomputing 69 (2006) 803-809
6. Zhu W., and Hu J. Stability analysis of stochastic delayed cellular neural networks by LMI approach. Chaos Solition Fract. 29 (2006) 171-174
7. Chen L., and Zhao H. New LMI conditions for global exponential stability of cellular neural networks with delays. Nonlin. Anal. Real World Appl. 10 (2009) 287-297
8. Singh V. Global robust stability of delayed neural networks: estimating upper limit of norm of delayed connection weight matrix. Chaos Solition Fract. 32 (2007) 259-263
9. Zheng C., Zhang H., and Wang Z. Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties. Neurocomputing 72 (2009) 1744-1754
10. Gau R., Lien C., and Hsieh J. Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach. Chaos, Solitons Frac. 32 (2007) 1258-1267
11. Wang Z., Liu Y., and Liu X. Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356 (2006) 346-352
12. Forti M., and Nistri P. Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Circuits Syst. I, Fundam. theory appl. 50 (2003) 1421-1435
13. Lu W., and Chen T. Dynamical behaviors of delayed neural network systems with discontinuous activation functions. Neural comput. 18 (2006) 683-708
14. Wang Y., et al. Global robust stability of delayed neural networks with discontinuous activation functions. IET Control Theory Appl. 7 (2008) 543-553
15. Forti M., Grazzini M., Nistri P., and Pancioni L. Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. IEEE Trans. Neural Network 214 (2006) 88-99
16. Lu W., and Chen T. Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Network 18 (2005) 231-242
17. Papini D., and Taddei V. Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations. Phys. Lett. A 343 (2005) 117-128
18. Tan M., and Tan Y. Global exponential stability of periodic solution of neural network with variable coefficients and time-varying delays. Appl. Math. Mod. 33 (2009) 373-385
19. Zuo Y., et al. Robust stability criterion for delayed neural networks with discontinuous activation functions. Neural Process. Lett. 29 (2009) 29-44
20. Singh V. Novel LMI condition for global robust stability of delayed neural networks. Chaos Solition Fract. 34 (2007) 503-508
21. Zuo Z., and Wang Y. Robust stability criterion for delayed cellular neural networks with norm-bounded uncertainties. IET Control Theory Appl. 1 (2007) 387-392
22. Singh V. LMI approach to the global robust stability of a larger class of neural networks with delay. Chaos Solition Fract. 32 (2007) 1927-1934
23. Wu W., and Cui B. Global robust exponential stability of delayed neural networks. Chaos Soliton Fract. 35 (2008) 747-754
24. Filippov A. Differential Equations with Discontinuous Right-Hand Side (1988), Kluwer Academic, Boston
25. Boyd S., et al. Linear Matrix Inequations in System and Control Theory (1994), SIAM, Philadelphia, PA
26. Liu X., and Cao J. On periodic solutions of neural networks via differential inclusions. Neural Networks 22 (2009) 329-334
27. Aubin J., and Cellina A. Differential Inclusions (1984), Springer, Berlin
28. Singh V. Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proc. Control Theory Appl. 151 (2004) 125-129
29. Cao J., and Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans. Circuits Syst. I Regular Papers 52 (2005) 417-426
30. A. Baciotti, R. Conti, P. Marcellini, Discontinuous ordinary differential equations and stabilization, Universita di Firenze, 2000.
31. Forti M., and Nistri P. Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Network 16 (2005) 1449-1463
32. Gu K., Kharitonov V., and Chen J. Stability of Time-Delay Systems (2003), Birkhauser, Boston, MA
33. Wang J., Huang L., and Guo Z. Dynamical behavior of delayed Hopfield neural networks with discontinuous activations. Appl. Math. Mod. 33 (2009) 1793-1802
34. Wu M., He Y., She J., and Liu G. Delay-dependent criteria for robust stability of time-varying delay systems. Auto. 40 (2004) 1435-1439
35. He Y., Wu M., She J., and Liu G. Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Sys. Control Lett. 51 (2004) 57-65
36. He Y., Wu M., She J., and Liu G. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans. Auto. Control 49 (2004) 828-832