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Mathematical Problems in Engineering
Volume 7 (2001), Issue 5, Pages 413-431
http://dx.doi.org/10.1155/S1024123X01001715

Absolute stability of nonlinear systems with time delays and applications to neural networks

1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
2Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Received 5 January 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.