Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations

Nonlinear Analysis: Real World Applications

Volumn 10, Issue 4, 2009, Pages 2297-2306

  Wu, Huaiqin ^a  

^a YANSHAN UNIVERSITY   (China)

Author keywords

Global exponential stability; Inverse Lipschitz functions; Matrix inequality; Neural networks; Neuron activation functions; Topological degree

Indexed keywords

CHEMICAL ACTIVATION; DIFFERENTIAL EQUATIONS; HOPFIELD NEURAL NETWORKS; LYAPUNOV FUNCTIONS; TIME VARYING NETWORKS;

GLOBAL EXPONENTIAL STABILITY; INVERSE LIPSCHITZ FUNCTIONS; MATRIX INEQUALITY; NEURON ACTIVATION FUNCTIONS; TOPOLOGICAL DEGREE;

NEURAL NETWORKS;

EID: 61849163302     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.04.016     Document Type: Article

References (15)

1. Arik S. An improved global stability result for delayed cellular neural networks. IEEE Trans. CAS-I 49 (2002) 1211-1214
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. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307 2-3 (2003) 136-147
4. Cao J., Liang J., and Lam J. Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199 (2004) 425-436
5. Deimling K. Nonlinear Functional Analysis (1985), Springer-Verlag, Berlin
6. Forti M., Manetti S., and Marini M. Necessary and sufficient condition for absolute stability of neural networks. IEEE Trans. Circuits Syst. I 41 (1994) 491-494
7. Forti M., and Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits. Syst. I 42 (1995) 354-366
8. Forti M., and Nistri P. Global convergence of neural networks with discontinuous neuron activation. IEEE Trans. Circuits. Syst. I 50 (2003) 1421-1435
9. Forti M., Nistri P., and Papini D. Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain. IEEE Trans. Neural Netw. 16 6 (2005) 1449-1463
10. Gahinet P., Nemirovski A., Laub J., and Chilali M. LMI Control Toolbox-for Use With Matlab (1995), The MATH Works, Inc., Natick, MA
11. Lu H., Chung F.L., and H Z. Some sufficient conditions for Global exponential stability of delayed Hopfield neural networks. Neural Netw. 17 (2004) 537-544
12. Lu W., and Chen T. Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions. Neural Netw. 18 (2005) 231-242
13. Miller P.K., and Michel A.N. Differential Equations (1982), Academic, New York
14. Qiao H., Peng J.G., and Xu Z. Nonlinear measures: A new approach to exponential stability analysis for Hopfield-type neural networks. IEEE Trans. Neural Netw. 12 (2001) 360-370
15. Zhang J., Suda Y., and Komine H. Global exponential stability of Cohen-Grossberg neural networks with variable delays. Phys. Lett. A 338 (2005) 44-50