Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-03-07 DOI:10.1137/22m1523066

Huabin Chen, Chenggui Yuan

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Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 924-952, April 2024.
Abstract. This paper provides some sufficient conditions for the existence and uniqueness and the stochastic stability of the global solution for nonlinear neutral stochastic functional differential equations. When the drift term and the diffusion term satisfy a locally Lipschitz condition, and the Lyapunov monotonicity condition has a sign-changed time-varying coefficient, the existence and uniqueness of the global solution for such equations will be studied by using the Lyapunov–Krasovskii function approach and the theory of stochastic analysis. The stability in [math]th-moment, the asymptotical stability in [math]th-moment, and the exponential stability in [math]th-moment will be investigated. Different characterizations for these three kinds of stochastic stability in moment will be established, which are presented with respect to integration conditions. These results have seldom been reported in the existing literature. The almost surely exponential stability for the global solution of such equations is also discussed. Some discussions and comparisons are provided. Two examples are given to check the effectiveness of the theoretical results obtained.

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非线性中性随机函数微分方程的稳定性分析

SIAM 控制与优化期刊》第 62 卷第 2 期第 924-952 页，2024 年 4 月。摘要本文为非线性中性随机函数微分方程全局解的存在性、唯一性和随机稳定性提供了一些充分条件。当漂移项和扩散项满足局部 Lipschitz 条件，且 Lyapunov 单调性条件具有符号时变系数时，将利用 Lyapunov-Krasovskii 函数方法和随机分析理论研究此类方程全局解的存在性和唯一性。将研究[math]th-moment 稳定性、[math]th-moment 渐进稳定性和[math]th-moment 指数稳定性。将建立这三种矩随机稳定性的不同特征，并根据积分条件加以介绍。这些结果在现有文献中鲜有报道。此外，还讨论了此类方程全局解的几乎肯定指数稳定性。还提供了一些讨论和比较。还给出了两个例子来检验所获得的理论结果的有效性。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.