Stabilization in distribution by discrete-time feedback control of hybrid delay systems with Lévy noise

Seyfeddine Moualkia, Yang Liu, Jianquan Lu, Jianlong Qiu

Abstract: This manuscript is concerned with a class of hybrid stochastic delay systems driven by Lévy noise (SDS-LN), where the coefficients are highly nonlinear. The key objective is to investigate the stabilization question of a given unstable SDS-LN via delayed discrete-time feedback controls. Under a set of appropriate assumptions and with the help of Lyapunov functional method, the existence of unique global solutions and its boundedness are showed. In addition, the stability in distribution of the controlled hybrid SDS-LN is discussed. As an application, we list an example attached with its corresponding numerical simulations to support the theoretical results.