Moment exponential stability of stochastic delay systems with delayed impulse effects at random times and applications in the stabilisation of stochastic neural networks

ABSTRACT

In this paper, we investigate the exponential stability for a class of impulsive stochastic functional differential equations with delayed impulse effects. The impulse instants considered in this paper are random times which are different from the existing literature. By using stochastic process theory, stochastic analysis theory, the Razumikhin technology and Lyapunov method, we derive some new criteria of the moment exponential stability for the suggested system. As an application, we obtain some new pinning impulsive control methods for the stabilisation of stochastic neural networks. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained results.

KEYWORDS:

• Stochastic delay system
• moment exponential stability
• delayed impulse effect
• random impulse instant
• stabilisation

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China (61374080,61773217), the China Postdoctoral Science Foundation (2018M632325), the Natural Science Foundation of Jiangsu Province (BK20161552), the Alexander von Humboldt Foundation of Germany (Fellowship CHN/1163390), Qing Lan Project of Jiangsu Province and the Priority Academic Program Development of Jiangsu Higher Education Institutions.