Delay-dependent asymptotic stability of highly nonlinear stochastic differential delay equations driven by G-Brownian motion

Based on the classical probability, the stability of stochastic differential delay equations (SDDEs) whose coefficientsare growing at most linearly has been investigated intensively. Moreover, the delay-dependent stability of highlynonlinear hybrid stochastic differential equations (SDEs) has also been studied recently. In this paper, using thenonlinear expectation theory, we first explore the delay-dependent criteria on the asymptotic stability for a class ofhighly nonlinear SDDEs driven by G-Brownian motion (G-SDDEs). Then, the (weak) quasi-sure stability of solutionsto G-SDDEs is developed. Finally, an example is analyzed by the φ-max-mean algorithm to illustrate our theoreticalresults