Stabilization of impulsive hybrid stochastic differential equations with Lévy noise by feedback control based on discrete-time state observations

In this paper, we investigate the problem of the mean-square exponential stabilization for a class of unstable impulsive hybrid stochastic differential equations with L & eacute;vy noise (IHSDEsLN) 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.