Asymptotical stability of stochastic neural networks with multiple time-varying delays

Abstract

The stochastic neural networks can be considered as an expansion of cellular neural networks and Hopfield neural networks. In real world, the neural networks are prone to be instable due to time delay and external disturbance. In this paper, we consider the asymptotic stability for the stochastic neural networks with multiple time-varying delays. By employing a Lyapunov-Krasovskii function, a sufficient condition which guarantees the asymptotic stability of the state trajectory in the mean square is obtained. The criteria proposed can be verified readily by utilising the linear matrix inequality toolbox in Matlab, and no parameters to be tuned. In the end, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Keywords:

• asymptotic stability
• stochastic neural networks
• multiple time-varying
• delays
• linear matrix inequality

Acknowledgements

The authors would like to thank the reviewers for their valuable comments and the Editor-in-Chief, Eric Rogers, for the hard work.

Additional information

Funding

This work is partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education [grant number 20120075120009]; the Key Foundation Project of Shanghai [grant number 12ZR1440200].