An LMI approach to global asymptotic stability of the delayed Cohen-Grossberg neural network via nonsmooth analysis

Neural Networks

Volumn 20, Issue 7, 2007, Pages 810-818

  Yu, Wenwu ^a,b   Cao, Jinde ^a   Wang, Jun ^c  

^a SOUTHEAST UNIVERSITY   (China)

^b Columbia University ^*  (United States)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Cohen Grossberg neural networks; Global asymptotic stability; LMI technique; Lyapunov functional method; Nonsmooth analysis; Time delay

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; FUNCTION EVALUATION; LINEAR MATRIX INEQUALITIES; TIME DELAY;

COHEN-GROSSBERG NEURAL NETWORKS; GLOBAL ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONAL METHOD; NONSMOOTH ANALYSIS;

NEURAL NETWORKS;

ANALYTIC METHOD; ARTICLE; ARTIFICIAL NEURAL NETWORK; COHEN GROSSBERG NEURAL NETWORK; LINEAR MATRIX INEQUALITY; NONSMOOTH ANALYSIS; PRIORITY JOURNAL; SIMULATION; STATISTICAL ANALYSIS; THEORETICAL MODEL; THEORETICAL STUDY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; INFORMATION STORAGE AND RETRIEVAL; LINEAR MODELS; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; PROGRAMMING, LINEAR; SIGNAL PROCESSING, COMPUTER-ASSISTED; SYSTEMS THEORY;

EID: 34548385611     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2007.07.004     Document Type: Article

References (38)

1. Arik S., and Orman Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays. Physics Letters A 341 (2005) 410-421
2. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear matrix inequalities in system and control theory (1994), SIAM, Philadelphia, PA
3. Cao J., and Liang J. Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays. Journal of Mathematical Analysis and Applications 296 (2004) 665-685
4. Cao J., and Song Q. Stability in Cohen-Grossberg type BAM neural networks with time-varying delays. Nonlinearity 19 (2006) 1601-1617
5. Cao J., and Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 50 (2003) 34-44
6. Cao J., and Wang J. Absolute exponential stability of recurrent neural networks with time delays and Lipschitz-continuous activation functions. Neural Networks 17 (2004) 379-390
7. Cao J., and Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 52 (2005) 417-426
8. Chen T., and Rong L. Delay-independent stability analysis of Cohen-Grossberg neural networks. Physics Letters A 317 (2003) 436-449
9. Chen Y. A remark on 'On stability of nonlinear continuous-time neural networks with delays'. Neural Networks 14 (2001) 1463
10. Clarke F.H. Optimization and nonsmooth analysis (1983), Wiley, New York
11. Cohen M.A., and Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics 13 (1983) 815-825
12. Joy M. On the global convergence of a class of functional differential equations with applications in neural network theory. Journal of Mathematical Analysis and Applications 232 (1999) 61-81
13. Liao T.L., and Wang F.C. Global stability for cellular neural networks with time delay. IEEE Transactions on Neural Networks 11 (2000) 1481-1484
14. Liao X.F., Li C., and Wong K. Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Networks 17 (2004) 1401-1414
15. Liao X.F., Wong K.W., Wu Z., and Chen G. Novel robust stability criteria for interval-delayed Hopfield neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48 (2001) 1355-1359
16. Lu H. On stability of nonlinear continuous-time neural networks with delays. Neural Networks 13 (2000) 1135-1143
17. Qi H., and Qi L. Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis. IEEE Transactions on Neural Networks 15 (2004) 99-109
18. Rockafellar R.T., and Wets R.J.B. Variational analysis (1998), Springer-Verlag, Berlin
19. Rong L. LMI-based criteria for robust stability of Cohen-Grossberg neural networks with delay. Physics Letters A 339 (2005) 63-73
20. Roska, T., & Chua, L.O. (1990). Cellular neural networks with nonlinear and delay-type template element. In Proc. 1st IEEE int. workshop cellular neural networks applicat. (pp. 12-15)
21. Singh V. A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Neural Networks 15 (2004) 223-225
22. Singh V. Global robust stability of delayed neural networks: An LMI approach. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 52 (2005) 33-36
23. Tu F., and Liao X.F. Harmless delays for global asymptotic stability of Cohen-Grossberg neural networks. Chaos, Solitons & Fractals 26 (2005) 927-933
24. Ye H., and Michel A.N. Robust stability of nonlinear time-delay systems with applications to neural networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 43 (1996) 532-543
25. Ye H., Michel A.N., and Wang K. Qualitive analysis of Cohen-Grossberg neural networks with multiple delays. Physical Review E 51 (1995) 2611-2618
26. Yu W. A LMI-based approach to global asymptotic stability of neural networks with time varying delays. Nonlinear Dynamics 48 (2007) 165-174
27. Yu, W. (in press). Robust control of delayed Cohen-Grossberg neural networks with time delays. International Journal of Adaptive Control and Signal Processing. doi: 10.1002/acs.963
28. Yu W., and Cao J. Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with time delays. Physics Letters A 351 (2006) 64-78
29. Yu W., and Cao J. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. Chaos 16 (2006) 023119
30. Yu W., and Cao J. Synchronization control of stochastic delayed neural networks. Physica A 373 (2007) 252-260
31. Yu W., and Cao J. Stability and Hopf Bifurcation on a two-neuron system with time delay in the frequency domain. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 (2007) 1355-1366
32. Yu, W., & Cao, J. (in press). Robust control of uncertain stochastic recurrent neural networks with time-varying delay. Neural Processing Letters. doi: 10.1007/s11063-007-9045-x
33. Yu W., Cao J., and Chen G. Robust adaptive control of unknown modified Cohen-Grossberg neural networks with delay. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 54 (2007) 502-506
34. Yu W., Chen G., Cao J., Lü J., and Parlitz U. Parameter identification of dynamical systems from time series. Physical Review E 75 (2007) 067201
35. Yu W., and Yao L. Global robust stability of neural networks with time varying delays. Journal of Computational and Applied Mathematics 206 (2007) 679-687
36. Yuan K., and Cao J. An analysis of global asymptotic stability of delayed Cohen-Grossberg neural networks via nonsmooth analysis. IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications 52 (2005) 1854-1861
37. Zeng Z., and Wang J. Global exponential stability of recurrent neural networks with time-varying delays in the presence of strong external stimuli. Neural Networks 19 (2006) 1528-1537
38. Zhang J., Suda Y., and Komine H. Global exponential stability of Cohen-Grossberg neural networks with variable delays. Physics Letters A 338 (2005) 44-50