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.

摘要

本文旨在设计基于过去状态的反馈控制来稳定一类由G-布朗运动驱动的非线性随机微分方程。通过建立延迟反馈控制和无延迟控制函数之间的联系，就时间延迟的大小建立了充分条件，确保了延迟反馈控制的p时刻指数稳定性和准指数稳定性系统。此外，还提供了确定时间延迟长度的上限以及进一步设计延迟反馈控制器的方法。给出了一个数值例子来证明我们的新理论。