Delay feedback stabilisation of stochastic differential equations driven by G-Brownian motion

ABSTRACT

This paper aims to design the feedback control based on past states to stabilise a class of nonlinear stochastic differential equations driven by G-Brownian motion. By building up the connection between the delay feedback control and the control function of no-delay, sufficient conditions are established in terms of size of the time delay ensuring both the pth moment exponential stability and quasi-surely exponential stability of the delay feedback controlled system. Moreover, methods for determining the upper bound of the length of the time delay and further designing the delay feedback controller are provided. A numerical example is presented to demonstrate our new theory.

KEYWORDS:

• G-Brownian motion
• pth moment exponential stability
• quasi-surely exponential stability
• delay feedback control

Acknowledgements

The authors would like to thank Professors Xuerong Mao, Liangjian Hu and Xiaoyue Li for their helpful comments and suggestions. The authors would also like to thank the Natural Science Foundation of China (71571001) for the financial support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [71571001].