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

Yin, Wensheng; Cao, Jinde; Ren, Yong

doi:10.1016/j.jmaa.2019.01.045

Cited by 31 publications

(6 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By applying aperiodically intermittent adaptive control, Li et al [14] concerned the stabilization of a stochastic complex system. Yin et al [36] studied quasisure exponential stabilization of a stochastic system induced by G-Brownian motion with discrete-time feedback control.…”

Section: Introductionmentioning

confidence: 99%

Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion

Wei

2022

Bound Value Probl

View full text Add to dashboard Cite

G-Brownian motion has potential applications in uncertainty problems and risk measures, which has attracted the attention of many scholars. This study investigates the almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion. Due to the non-linearity of G-expectation and distribution uncertainty of G-Brownian motion, it is difficult to study this issue. Firstly, the existence of the global unique solution is derived under the linear growth condition and local Lipschitz condition. Secondly, the almost sure exponential stability of the system is analyzed by applying the G-Lyapunov function and G-Itô formula. Finally, an example is introduced to illustrate the stability. The conclusions of this paper can be applied to the stability and risk management of uncertain financial markets.

show abstract

Section: Introductionmentioning

confidence: 99%

Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion

Wei

2022

Bound Value Probl

View full text Add to dashboard Cite

show abstract

“…In the G-framework, Zhang and Chen [31] considered the quasi-sure exponential stability of semi-linear G-SDEs. By means of G-Lyapunov function method, Li et al [13], Ren et al [22], and Yin et al [30] established the moment stability and the quasi-sure stability for nonlinear G-SDEs.…”

Section: Introductionmentioning

confidence: 99%

On the averaging principle for SDEs driven by G-Brownian motion with non-Lipschitz coefficients

2021

View full text Add to dashboard Cite

In this paper, we aim to develop the averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs for short) with non-Lipschitz coefficients. By the properties of G-Brownian motion and stochastic inequality, we prove that the solution of the averaged G-SDEs converges to that of the standard one in the mean-square sense and also in capacity. Finally, two examples are presented to illustrate our theory.

show abstract

“…Thereafter, its related stochastic calculus, strong laws of large numbers, and central limit theorem under sublinear expectation have been established [4][5][6][7][8]. Especially, based on sample path properties of G-Brownian motion, many studies are available discussing the stochastic differential equation driven by G-Brownian motion (GSDEs) [9][10][11][12][13]. For example, Gao [9] studied the existence for the solutions of GSDEs under Lipschitz coefficient.…”

Section: Introductionmentioning

confidence: 99%

Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion

2020

Self Cite

View full text Add to dashboard Cite

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. disturbance and reduce the influence of the impulsive effect. [24,25] established the stability for impulsive stochastic differential equations driven by G-Brownian motion with the help of G-Lyapunov function technique. In the evolution of dynamical systems, it is impossible for systems to contact at the same time owing to time-delays. To get over the adverse impact of time-delays, delay-dependent scheme is a vigorous tool to verify the stability of dynamical systems (see [26][27][28]).To our best knowledge, there is no literature reported on the pth moment exponential stability and quasi sure exponential stability of the zero solution for impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs) or impulsive stochastic delayed differential systems driven by G-Brownian motion. Therefore, the influence of between delay and impulse for stochastic systems driven by G-Brownian motion provide a motivation of the current study. The aim of this paper is to investigate G-Lyapunov method for IGSFDSs. The contributions in this paper are concluded as follows: (i) Some theorems on pth moment exponential stability and quasi sure exponentially stability of the zero solution of IGSFDSs are established by G-Lyapunov method and impulsive analysis. (ii) These new results are employed to impulsive stochastic delayed systems driven by G-Brownian motion. (iii) If the upper bound of delay may not surpass the length of impulsive gap, delay-dependent technique is utilized to get over the influences of impulses and time delay by G-Lyapunov-Krasovkii functional. The remaining part of this paper is arranged as follows. In Section 2, some definitions and lemmas on G-expectation are proposed and the model descriptions of IGSFDSs are presented. In Section 3, some pth moment exponential stability and quasi sure exponential stability criteria are obtained via stochastic analysis and impulse technique. Section 4 extends the above theorems to impulsive stochastic delayed differential systems driven by G-Brownian motion. In addition, delay-dependent method is employed to establish the stability theorem. In Section 5, an example is provided to show our results. Section 6 gives some conclusions.

show abstract

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

Cited by 31 publications

References 31 publications

Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion

Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion

On the averaging principle for SDEs driven by G-Brownian motion with non-Lipschitz coefficients

Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion

Contact Info

Product

Resources

About