Global stability analysis for a class of neural networks with varying delays and control input

Applied Mathematics and Computation

Volumn 189, Issue 2, 2007, Pages 1480-1490

  Cao, Jiuwen ^a   Zhong, Shouming ^a   Hu, Yuanyuan ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Control input; Global stability; Liapunov Krasovskii functions; Neutral systems; Razumikhin's method; Varying delays

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; NONLINEAR EQUATIONS; SYSTEM STABILITY;

CONTROL INPUT; GLOBAL STABILITY; LIAPUNOV-KRASOVSKII FUNCTIONS; NEUTRAL SYSTEMS; RAZUMIKHIN'S METHOD; VARYING DELAYS;

NEURAL NETWORKS;

EID: 34249035262     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.12.048     Document Type: Article

References (21)

1. Chua L.O., and Yang L. Cellular neural networks: applications. IEEE Trans. Circuits Syst. 35 (1988)
2. Cichocki A., and Unbehauen R. Neural Networks for Optimization and Signal Processing (1993), Wiley, Chichester
3. Michel A.N., and Liu D. Qualitative Analysis and Synthesis of the Recurrent Neural Networks (2002), Marcel Dekker, New York
4. Hirsch M.W. Convergent activation dynamics in continuous time networks. Neural Networks 2 (1989)
5. Kaszkurewicz E., and Bhaya A. On a class of globally stable neural circuits. IEEE Trans. Circuits Syst. I 41 (1994)
6. Xu S., Lam J., Ho D.W.C., and Zou Y. Global robust exponential stability analysis for interval recurrent neural networks. Phys. Lett. A 325 (2004)
7. Arik S. Global asymptotic stability of a larger class of neural networks with constant time delays. Phys. Lett. A 311 (2003)
8. Cao J., and Zhou D. Stability analysis of delayed cellular neural networks. Neural Networks 11 (1998)
9. Joy M. On the global convergence of a class of functional differential equations with applications in neural network theory. J. Math. Anal. Appl. 232 (1999)
10. Van Den Driessche P., and Zou X. Global attractivity in delayed Hopfield neural networks models. SIAM J. Appl. Math. 6 (1998)
11. Zhang J. Global stability analysis in delayed cellular neural networks. Comput. Math. Appl. 45 (2003)
12. Hale J.K. Theory of Functional Differential Equations (1977), Springer, New York
13. Bamett S. Polynomials and Linear Control Systems (1983), Marcel Dekker, New York
14. Hu G.-D., and Hu G.-D. Some simple criteria for stability of neutral delay differential systems. Appl. Math. Comput. 80 (1996) 257-271
15. Niculescu S.-I. Delay Effects on Stability (2001), Springer, Berlin
16. Stoinski U. Delay-independent stability criteria for neutral differential equations. Differ. Integral Equat. 7 (1994) 593-599
17. Bellen A., Guglielmi N., and Ruehli A.E. Methods for linear systems of circuit delay differential equations of neutral type. IEEE Trans. Circuits Syst. I CAS-46 (1999) 212-216
18. Khusainov D.Y., and Yunkova E.A. Investigation of the stability of linear-systems of neutral type by the Lyapunov function method. Differ. Equat. 24 (1988) 424-431
19. Fridman E. Nea Lyapunov Krasovskii functionals for stability of linear retarded and neutral type systems. Syst. Control Lett. 43 (2001) 309-319
20. Ensari T., and Arik S. Global stability analysis of neutral networks with multiple time varying delays. IEEE Trans. Automat. Control 50 11 (2005) 1781-1785
21. Kolmanovskii V., and Myshkis A. Introduction to the Theory and Applications of Functional Differential Equations (1992), Kluwer Academic Publishers, Dordrecht