This paper is devoted to deal with the stabilisation problems of continuous-time hybrid stochastic systems (often described by stochastic differential equations with Markovian switching) with Lévy noise by feedback controls based on discrete-time state observations. There are so far few results on the stabilisation of continuous-time hybrid stochastic systems with Lévy noise based on discrete-time state observations, despite the stabilisation of stochastic systems by discrete-time feedback controls has been investigated in general. Precisely, it is discussed the stabilisation in the sense of $H_{\mathrm{\infty }}$-stability, asymptotic stability, mean-square exponential stability and almost sure exponential stability for such systems. It is also presented an upper bound on the duration τ between two consecutive state observations by means of the Lyapunov function. Two examples are given to illustrate the obtained results.

本文致力于通过基于离散时间状态观测的反馈控制来处理具有 Lévy 噪声的连续时间混合随机系统（通常由带有马尔可夫切换的随机微分方程描述）的镇定问题。尽管已经普遍研究了通过离散时间反馈控制来稳定随机系统，但迄今为止，关于基于离散时间状态观测的具有 Lévy 噪声的连续时间混合随机系统的稳定性的结果很少。确切地说，它是在讨论的意义上的稳定$H_{\mathrm{\infty }}$-稳定性，渐近稳定性，均方指数稳定性和此类系统的几乎确定的指数稳定性。它还通过李雅普诺夫函数给出了两个连续状态观测之间的持续时间τ的上限。给出两个例子来说明得到的结果。