Exponential stability and global stability of cellular neural networks

Applied Mathematics and Computation

Volumn 147, Issue 3, 2004, Pages 843-853

  Li, Xuemei ^a,b   Huang, Lihong ^a  

^a HUNAN UNIVERSITY   (China)

^b HUNAN NORMAL UNIVERSITY   (China)

Author keywords

Cellular neural networks; Completely stable matrix; Exponential stability; Global stability; Strongly stable matrix

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; GLOBAL OPTIMIZATION; MATRIX ALGEBRA; PROBLEM SOLVING; THEOREM PROVING;

GLOBAL STABILITY;

CELLULAR NEURAL NETWORKS;

EID: 0141886349     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00816-0     Document Type: Article

References (14)

1. Forti M., Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. 42:1995;354-366.
2. Liao X. Mathematical theory of cellular neural networks (I). Sci. China (series A). 24:1994;902-910.
3. Fiedler M., Ptak V. Some generalizations of positive definiteness and monotonicity. Numer. Math. 9:1966;163-172.
4. Halanay A., Rasvan V. Applications of Liapunov Methods in Stability. 1993;Kluwer Academic Publishers.
5. Hershkowitz D. Recent directions in matrix stability. Linear Algebra Appl. 171:1992;161-186.
6. Berman A., Shasha D. Inertia-preserving matrices. SIAM J. Matrix Anal. Appl. 12:1991;209-219.
7. Chua L.O., Yang L. Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35:1988;1257-1272.
8. Roska T., Vandewalle J. Cellular Neural Networks. 1995;Wiley, New York.
9. Wu C.W., Chua L.O. More rigorous proof of complete stability of cellular neural networks. IEEE Trans. Circuits Syst. 44:1997;370-371.
10. Gilli M. Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Trans. Circuits Syst. 41:1994;518-528.
11. Chua L.O., Roska T. Stability of a class of nonreciprocal cellular neural networks. IEEE Trans. Circuits Syst. 37:1990;1520-1527.
12. Chua L.O., Wu C.W. The universe of stable CNN templates. Int. J. Circuit Theory Appl. 20:1992;497-517.
13. Takahashi N., Chua L.O. On the complete stability of nonsymmetric cellular neural networks. IEEE Trans. Circuits Syst. 45:1998;754-758.
14. Arik S., Tavsanoglu V. Equilibrium analysis of nonsymmetric CNNs. Int. J. Circuit Theory Appl. 24:1996;269-274.