Quasi-sure exponential stability and stabilisation of stochastic delay differential equations under G-expectation framework

Abstract

In this work, we obtain the sufficient conditions to examine quasi-sure exponential stability of stochastic delay differential equation under G-expectation framework (in short, G-SDDE). Our argument is based on quasi-sure exponential stability of G-SDE and we should point out that the keys to the proof of our main result are the fact that there exists a positive number such that the G-SDDE is also quasi-surely exponentially stable as long as the time delay constant . Furthermore, this approach allows to design the delay feedback control induced by G-Brownian motion so as to stabilise the given deterministic systems in terms of quasi-sure exponential stability.