Stabilization of stochastic differential equations driven by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>G</mml:mi></mml:math>-Brownian motion with feedback control based on discrete-time state observation

Ren, Yong; Yin, Wensheng; Sakthivel, R.

doi:10.1016/j.automatica.2018.05.039

Cited by 70 publications

(40 citation statements)

References 12 publications

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“…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%

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

2020

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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.

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Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

2020

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“…The existence theory and estimates for the difference between exact and approximate solutions of stochastic differential equations driven by G-Brownian motion can be found in [2,8,9]. Also see [21][22][23][24][25][26]. Unlike to the above briefly discussed literature, this article presents the study of G-NSFDEs with some suitable monotone type conditions in the phase space C q defined below.…”

Section: Introductionmentioning

confidence: 99%

On boundedness and convergence of solutions for neutral stochastic functional differential equations driven by G-Brownian motion

Faizullah

2019

Adv Differ Equ

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The current article presents the study of neutral stochastic functional differential equations driven by G-Brownian motion in the phase space C q ((-∞, 0]; R n ). The mean-square boundedness of solutions has been derived. The convergence of solutions with different initial data has been investigated. The boundedness and convergence of solution maps have been obtained. In addition, the L 2 G and exponential estimates of solutions have been determined. MSC: 60H20; 60H10; 60H35; 62L20

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“…Ren, Jia, and Sakthivel (2016) discussed the pth moment stability of solutions to impulsive G-SDEs. Moreover, some other important properties of G-SDEs have been investigated by many researchers (see Deng, Fei, Fei, & Mao, 2019;Faizullah, 2016;In Press;Hu, Lin, & Hima, 2018;Li & Yang, 2018;Luo & Wang, 2014;Ren et al, 2016;Ren, Yin, & Sakthivel, 2018;Yin, Cao, & Ren, 2019;Yin & Ren, 2017). Mao (2002); Mao and Rassias (2005) established a Khasminskii-type test for SDDEs.…”

Section: Introductionmentioning

confidence: 99%

Khasminskii-type theorems for stochastic differential delay equations driven by G-Brownian motion

Liang

Chen

2019

Systems Science & Control Engineering

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The Khasminskii theorem have come to play an important role in the nonexplosion solutions of stochastic differential equations (SDEs) without the linear growth condition. In this paper, by using Peng's G-expectation theory, we establish an even more general Khasminskii-type test for stochastic differential delay equations driven by G-Brownian motion (G-SDDEs) that cover a wide class of highly nonlinear G-SDDEs.

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Stabilization of stochastic differential equations driven by G-Brownian motion with feedback control based on discrete-time state observation

Cited by 70 publications

References 12 publications

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

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

On boundedness and convergence of solutions for neutral stochastic functional differential equations driven by G-Brownian motion

Khasminskii-type theorems for stochastic differential delay equations driven by G-Brownian motion

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