Delay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion

Abstract

This study discusses delay-dependent stability of a class of stochastic delay systems driven by G-Brownian motion in the sublinear expectation space. With the help of the degenerate Lyapunov functional, the mean square exponential stability and quasi-sure exponential stability criteria for stochastic delay systems driven by G-Brownian motion are established and an explicit upper bound of time delay is derived. In particular, for the delay-free case, the corresponding sufficient conditions are also obtained. Here, the stability conditions are directly related to the coefficients of the stochastic delay systems and are different from the existing stability conditions which are presented in terms of the G-Lyapunov function. Some examples are introduced to illustrate the delay-dependent stability criteria.