This work establishes a “robustness” type result, namely, delay tolerance for stable stochastic systems under suitable conditions. We study the delay tolerance for stable stochastic systems and delayed feedback controls of such systems, where the delay can be state-dependent or induced by the sampling-data. First, we consider systems with global Lipschitz continuous coefficients and show that when the original stochastic system without delay is pth moment exponentially stable, the system with small delays is still pth moment exponentially stable. In particular, when the pth moment exponential stability is based on Lyapunov conditions, we can obtain explicit delay bounds for moment exponential stability. Then, we consider a class of stochastic systems with non-global Lipschitz conditions and find a delay bound for almost sure and mean square exponential stability. As extension of the stability tolerance criteria, consensus and tracking control of multi-agent systems with measurement noises and nonuniform delays are studied.

中文翻译：

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稳定随机系统和扩展的延迟容限

这项工作建立了一个“稳健性”类型的结果，即在合适条件下稳定随机系统的延迟容限。我们研究稳定随机系统的延迟容限和此类系统的延迟反馈控制，其中延迟可以是状态相关的或由采样数据引起的。首先，我们考虑具有全局Lipschitz 连续系数的系统，并证明当原始无延迟随机系统是第p 阶矩指数稳定的时，具有小延迟的系统仍然是第p 阶矩指数稳定的。特别是，当第 p 阶矩指数稳定性基于李雅普诺夫条件时，我们可以得到矩指数稳定性的显式延迟界。然后，我们考虑一类具有非全局 Lipschitz 条件的随机系统，并找到几乎肯定和均方指数稳定性的延迟界限。作为稳定性容忍标准的扩展，研究了具有测量噪声和非均匀延迟的多智能体系统的一致性和跟踪控制。