Quasi-sure exponential stabilization of stochastic systems induced by G-Brownian motion with discrete time feedback control

Abstract

In this paper, we aim to study quasi-sure exponential stabilization of stochastic systems induced by G-Brownian motion with discrete time feedback control. As for an unstable system, we use discrete stochastic feedback control to stabilize it. If stochastic differential equation driven G-Brownian motion (G-SDE, in short) is quasi-sure exponential stability, it reveals that there exist the discrete step size h>0 and a positive constant h˜ with h<h˜, and the responding stochastically controlled system is also quasi-sure exponential stability. Finally, a simple example is also provided to show the validity of the control strategy.