Stability analysis of neutral stochastic delay differential equations by a generalisation of Banach's contraction principle

ABSTRACT

In this paper, we consider a class of neutral stochastic differential systems with variable delays and give sufficient conditions to ensure that the zero solution is asymptotically stable in the mean square by means of a generalisation of Banach's contraction principle. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. The results are shown to improve the previous globally stable results derived in the literature.

KEYWORDS:

• Neutral stochastic differential system
• fixed points
• stability
• variable delays

MSC:

• 34K20
• 34K13
• 92B20

Acknowledgments

The authors sincerely thank the anonymous reviewer for his or her careful reading, constructive comments and suggestions for improving the quality of the manuscript. This work was partially supported by the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China (No.ICT1544), the National High Technology Research and Development Program of China (2012AA041701) and the Postdoctoral Science Foundation of China (2014M551738).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China [grant number ICT1544]; the National High Technology Research and Development Program of China [grant number 2012AA041701]; the Postdoctoral Science Foundation of China [grant number 2014M551738].