Stabilization of unstable impulsive systems via stochastic discrete-time feedback control with Lévy noise

Abstract

It is universally acknowledged that noise can stabilize systems. Given an unstable impulsive system, can it be stabilized by Lévy noise? In this article, we mainly discuss the stochastic stabilization of unstable impulsive systems via Lévy noise. First, the conditions for $p$-moment exponential stability of unstable impulsive systems under continuous-time feedback control with Lévy noise are derived using the Lyapunov function method. Second, the almost sure exponentially stable conditions for the unstable impulsive systems under discrete-time feedback control with Lévy noise are derived through the comparison method. Additionally, several new stochastic stabilization strategies are proposed to design stochastic discrete-time feedback control for deriving almost sure exponentially stable results through stochastic analysis. Finally, two examples and their relevant simulation figures are given to check the validity of the results.