Almost sure and moment asymptotic boundedness of stochastic delay differential systems

Xu, Liguang; Dai, Zhenlei; Hu, Hongxiao

doi:10.1016/j.amc.2019.05.027

Cited by 10 publications

(7 citation statements)

References 19 publications

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“…Here, we choose λ 0 = 0.9 and λ = 0.5 < λ 0 which satisfies the inequality (6). According to Theorem 3.1, system (33) is GEUB in the mean square, and the solutions y(t) will converge to the ultimate bound set…”

Section: An Example Example 41mentioning

confidence: 99%

“…Recently, the study of the boundedness of dynamical systems has attracted increasing attention from researchers since it plays a key role in the analysis of the stability, existence, persistence, chaotic behaviour, attracting properties and other properties of the solutions. Many significant results on the boundedness have been established for various systems such as stochastic delay differential systems [4][5][6][7], non-autonomous neural networks [8,9], non-linear switched systems [10], integro-differential systems [11][12][13], impulsive stochastic systems [14][15][16], impulsive fractional differential systems [17][18][19], impulsive fractional difference systems [20], impulsive differential systems [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Boundedness analysis of stochastic integro-differential systems with Lévy noise

2019

Journal of Taibah University for Science

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This paper is concerned with the pth moment globally exponential ultimate boundedness of stochastic integro-differential systems with Lévy noise. With the help of the Lyapunov function methods and the inequality techniques, several sufficient criteria on the exponential ultimate boundedness are presented for the systems. The results show that the boundedness was determined by the coefficients in the estimation of the Itô operator LV of the energy function V along the trajectories of the addressed systems. ARTICLE HISTORYwhere the scalar λ satisfies 0 < λ < λ 0 and is determined by (25). This concludes the proof of the result. Corollary 3.3:Suppose that the hypotheses of Theorem 3.1 hold. If 5 = 0, then system (1) is pth moment globally exponentially stable (p-GES).Proof: This result follows directly from Theorems 3.1.Corollary 3.4: Suppose that the Assumption 3.1 with K 3 = K 6 = K 9 = K 12 = 0 holds. Ifˆ 3 >ˆ 4 > 0, then system (1) is p-GES.Proof: This result follows directly from Theorems 3.2.

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Section: An Example Example 41mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boundedness analysis of stochastic integro-differential systems with Lévy noise

2019

Journal of Taibah University for Science

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“…As far as we know, there are fruitful research works on SDEs driven by Brownian motion, see refs. [2–5, 7, 10–14, 16]. However, due to large internal or external fluctuations, there may be some jump random perturbations in the actual system.…”

Section: Introductionmentioning

confidence: 99%

“…To mention a few, ref. [4] has developed some sufficient criteria to ensure the asymptotic boundedness (AB), the asymptotic stability (AS) and the exponential stability (ES) for non-autonomous SDDEs. In ref.…”

Section: Introductionmentioning

confidence: 99%

Boundedness and stability of nonlinear hybrid stochastic differential delay equation disturbed by Lévy noise

Yang

Chen

2022

IET Control Theory & Appl

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This study focuses on the boundedness and stability of the nonlinear hybrid stochastic differential delay equation (NHSDDE) disturbed by Lévy noise (LN). Different from the previous systems with Markovian switching, not only different parameters under different modes, but also different structures under different modes are considered, where a novel Lyapunov function is constructed to handle the impacts of different structures under different modes. Without the linear growth condition, the existence of the global solution is proved for the NHSDDE with LN. Then, the M‐matrix technique is applied to build some reasonable theorems upon the vth moment asymptotic boundedness, the vth moment exponential stability and the almost surely exponential stability for the NHSDDE driven by LN. An approach to solving the admissible upper bound of the time‐delay derivative is given for guaranteeing the asymptotic boundedness and the exponential stability of the global solution. Finally, two numerical examples and homologous simulated outcomes are provided to indicate the usefulness of the presented theoretical findings.

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“…There are many works on impulsive systems with stochastic factors (e.g. [32], [34], [35]), but, as far as we know, there is little literature on the roles of stochastic noises on the dynamic behavior of impulsive differential systems. According, there is a tremendous blank about it.…”

Section: Introductionmentioning

confidence: 99%

Noises for Impulsive Differential Systems

Hao

Feng

2019

IEEE Access

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Stochastic feedback control has aroused folks' notice, but little is known on the roles of stochastic noises for the dynamic behavior of impulsive differential systems. In this paper, we mainly study the problem of stochastic stabilization on explosive solutions of nonlinear impulsive differential systems by noises. Under the one-sided polynomial growth condition, a nonlinear impulsive differential system may explode at a finite time. To suppress the explosive solution, we introduce two independent stochastic noises (polynomial and linear) such that there exists a unique global solution for the corresponding stochastically perturbed impulsive differential system, and the global solution is bounded and almost surely exponentially stable.

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Almost sure and moment asymptotic boundedness of stochastic delay differential systems

Cited by 10 publications

References 19 publications

Boundedness analysis of stochastic integro-differential systems with Lévy noise

Boundedness analysis of stochastic integro-differential systems with Lévy noise

Boundedness and stability of nonlinear hybrid stochastic differential delay equation disturbed by Lévy noise

Noises for Impulsive Differential Systems

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