Abstract This paper is devoted to study the p th moment exponential stability problem for a class of stochastic delay nonlinear systems (SDNSs) driven by G-Brownian motion. The delays considered in this paper are time-varying delays τ i ( t ) ∈ [ 0 , τ ] ( 1 ≤ i ≤ 3 ) and they are not required to be differentiable. Different from the traditional methods, we use a new approach: stochastic delay feedback controls. We firstly compare the SDNS with the corresponding stochastic nonlinear system (SNS) instead of studying the stability of the SDNS directly. Then, we impose the condition on the SNS to ensure the p th moment exponential stability of the SNS. Furthermore, we show that there is a positive constant τ ∗ such that the SDNS is also p th moment exponentially stable provided τ τ ∗ . In particular, we give an implicit lower bound for τ ∗ which can be computed numerically.

中文翻译：

---

G-布朗运动驱动的一类随机延迟非线性系统的稳定性分析

摘要 本文致力于研究G-布朗运动驱动的一类随机延迟非线性系统(SDNS)的p阶矩指数稳定性问题。本文中考虑的时滞是时变时滞τ i ( t ) ∈ [ 0 , τ ] ( 1 ≤ i ≤ 3 ) 并且它们不需要是可微的。与传统方法不同，我们使用了一种新方法：随机延迟反馈控制。我们首先将 SDNS 与相应的随机非线性系统 (SNS) 进行比较，而不是直接研究 SDNS 的稳定性。然后，我们对 SNS 施加条件以确保 SNS 的 p 阶矩指数稳定性。此外，我们表明存在一个正常数 τ ∗ 使得 SDNS 在 τ τ ∗ 的情况下也是 p 阶矩指数稳定的。特别是，