Improved asymptotic stability conditions for neural networks with discrete and distributed delays

Abstract

This paper considers the asymptotic stability problem for a class of neural networks with discrete and distributed delays. Based on a new augmented Lyapunov functional and integral inequalities, the new asymptotic stability condition is established in terms of linear matrix inequality. Meanwhile, the importance of some augmented terms in the Lyapunov functional are discussed. Compared with previous methods to deal with the distributed delay, our method is less conservative due to the use of the new Lyapunov functional. Finally, numerical examples illustrate the relaxation of obtained results and our claims.

Keywords:

• asymptotic stability
• neural networks
• discrete and distributed delays
• augmented Lyapunov functional
• linear matrix inequality

2000 AMS Subject Classifications::

• 34K20
• 92B20

Acknowledgements

This work was partly supported by National Natural Science Foundations of PR China under Grants 60835001, 61174076 and 61104068. This work was also partly supported by the Research Foundations for the Doctoral Program of Higher Education of PR China under Grants 20090092120027 and 20110092110021. The authors thank the editors and anonymous reviewers for their constructive comments in improving the presentation and quality of this manuscript. Finally, the authors express their appreciation to Yunbing Xin (vice professor) for his suggestions in revising the manuscript.