Abstract
This paper is concerned with the p-th moment exponential stability and quasi sure exponential stability of impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs). By using G-Lyapunov method, several stability theorems of IGSFDSs are obtained. These new results are employed to impulsive stochastic delayed differential systems driven by G-motion (IGSDDEs). In addition, delay-dependent method is developed to investigate the stability of IGSDDSs by constructing the G-Lyapunov–Krasovkii functional. Finally, an example is given to demonstrate the effectiveness of the obtained results.
Highlights
In the past few decades, stochastic differential system has been widely applied to engineering science, electricity and economics [1,2]
In [11], by using discrete time feedback control, the authors discussed stabilization of stochastic systems driven by G-Brownian motion
Consider the following impulsive stochastic delayed differential systems driven by G-Brownian motion (IGSDDSs):
Summary
In the past few decades, stochastic differential system has been widely applied to engineering science, electricity and economics [1,2]. G-expectation is a rising research owing to inclusive application in risk measures, volatility uncertainty, superpricing in finance, and so on. G-expectation can be traced back to Peng [3], where G is an infinitesimal generator of a heat equation. G-Brownian motion, many studies are available discussing the stochastic differential equation driven by G-Brownian motion (GSDEs) [9,10,11,12,13]. In [10], a Lyapunov differential operator under G-expectation is provided to deal with G-martingale problems. In [11], by using discrete time feedback control, the authors discussed stabilization of stochastic systems driven by G-Brownian motion
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