In this paper, we investigate the problem of the mean-square exponential stabilization for a class of unstable impulsive hybrid stochastic differential equations with Lévy noise (IHSDEs-LN) via feedback control based on discrete-time state observations. Our results show that if feedback control of continuous-time observations can stabilize the controlled system in the sense of mean-square exponential stability, then feedback control of discrete-time state observations can also stabilize the controlled system. And there exists an upper bound on the interval between adjacent observation moments that can be accurately computed. Based on this new theory, we first design continuous-time feedback control for unstable IHSDEs-LN to achieve the stabilization problem, and then improve the continuous-time feedback control to discrete-time state observations feedback control.

中文翻译：

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基于离散时间状态观测的反馈控制具有 Lévy 噪声的脉冲混合随机微分方程的稳定性


在本文中，我们通过基于离散时间状态观测的反馈控制，研究了一类带有 Lévy 噪声的不稳定脉冲混合随机微分方程（IHSDE-LN）的均方指数稳定性问题。我们的结果表明，如果连续时间观测的反馈控制可以在均方指数稳定性意义上稳定受控系统，那么离散时间状态观测的反馈控制也可以稳定受控系统。并且相邻观测时刻之间的间隔存在一个可以精确计算的上限。基于这一新理论，我们首先针对不稳定的IHSDE-LN设计连续时间反馈控制来实现镇定问题，然后将连续时间反馈控制改进为离散时间状态观测反馈控制。