共查询到20条相似文献,搜索用时 31 毫秒
1.
随机时变线性系统的稳定性 总被引:1,自引:0,他引:1
利用构造二次型Lyapunov函数和Ito公式研究了一般n维时变线性Ito型随机微分系统的稳定性,给出了二维时变线性系统的三种常见情形的均方指数 稳定或均方渐近稳定的充分判据。 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(5):1391-1399
A stochastic one-dimensional Gilpin–Ayala model driven by Lévy noise is presented in this paper. Firstly, we show that this model has a unique global positive solution under certain conditions. Then sufficient conditions for the almost sure exponential stability and moment exponential stability of the trivial solution are established. Results show that the jump noise can make the trivial solution stable under some conditions. Numerical example is introduced to illustrate the results. 相似文献
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通过使用灰色矩阵覆盖集的分解方法和矩阵范数的性质,构造李雅普诺夫函数,研究了灰色中立随机线性时滞系统的鲁棒稳定性和几乎指数鲁棒稳定性. 相似文献
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把Peuteman-Aeyels指数稳定性定理从确定性系统推广到随机系统.并借此讨论了随机混杂系统的均方指数镇定问题,得出了系统在同步切换下可镇定的充分必要条件. 相似文献
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研究了一类非线性中立型随机微分系统的稳定性问题.该类非线性随机微分系统不仅包含系统的过去状态,而且还和系统的过去时刻的运动特性相关,同时,还具有Markov跳变参数.利用所定义的广义Ito微分公式,通过构造适当随机Lyapunov泛函,给出了此类随机系统的均方指数稳定性的充分条件.该条件放宽了已有结果的限制,具有更加广泛的适用范围.同时,还给出了此类随机系统的几乎必然指数稳定性的充分条件. 相似文献
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In this work, we investigate stochastic partial differential equations with variable delays and jumps. We derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions, and generalize the results obtained by Taniguchi [T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl. 331 (2007) 191-205] and Wan and Duan [L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory, Statist. Probab. Lett. 78 (5) (2008) 490-498] to cover a class of more general stochastic partial differential equations with jumps. Finally, an illustrative example is established to demonstrate our established theory. 相似文献
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Razumikhin method to global exponential stability for coupled neutral stochastic delayed systems on networks 下载免费PDF全文
Global exponential stability for coupled neutral stochastic delayed systems on networks (CNSDSNs) is investigated in this paper. By means of combining the Razumikhin method with graph theory, some sufficient conditions that can be verified easily are derived to ensure the global exponential stability for CNSDSNs. Finally, a specific model of CNSDSNs is discussed, and numerical test manifests the effectiveness of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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Svetlana Jankovi? 《Journal of Mathematical Analysis and Applications》2009,355(2):811-6134
The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(1):128-138
In this paper, we analyze the robustness of global exponential stable stochastic delayed systems subject to the uncertainty in parameter matrices. Given a globally exponentially stable systems, the problem to be addressed here is how much uncertainty in parameter matrices the systems can withstand to be globally exponentially stable. The upper bounds of the parameter uncertainty intensity are characterized by using transcendental equation for the systems to sustain global exponential stability. Moreover, we prove theoretically that, the globally exponentially stable systems, if additive uncertainties in parameter matrices are smaller than the upper bounds arrived at here, then the perturbed systems are guaranteed to also be globally exponentially stable. Two numerical examples are provided here to illustrate the theoretical results. 相似文献
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研究了一类G-Brown运动驱动的中立型随机时滞微分方程的指数稳定性.在G-框架意义下,运用合适的Lyapunov-Krasovskii泛函,中立型时滞微分方程理论以及随机分析技巧,证明了所研究方程平凡解的p-阶矩指数稳定性,得到了所研究方程平凡解是p-阶矩指数稳定的充分条件.最后通过例子说明所得的结果. 相似文献
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By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory. 相似文献
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吴述金 《数学物理学报(A辑)》2005,25(6):789-798
该文首先给出了具有随机脉冲时刻影响的非线性微分系统 模型,然后得到了该模型零解的p阶矩指数稳定和几乎必然指数稳定的充分条件,在所得结果中不要求dV(t,x(t)) /dt定负.最后,给出一个例子说明所得结果的应用. 相似文献
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Haiyan Yuan 《计算数学(英文版)》2022,40(2):177-204
In this paper, the numerical methods for semi-linear stochastic delay integro-differential equations are studied. The uniqueness, existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with strong order $\frac{1}{2}$ and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results. 相似文献
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由于流体受到某些遗传和不确定信息外力的影响,考虑了含时变时滞随机外力的2D-Navier-Stokes方程.借助随机分析中的It6公式和Burkholder-Davis-Gundy不等式,证明了大粘性系数情形方程整体弱解的均方指数稳定和几乎必然指数稳定. 相似文献
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Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach 下载免费PDF全文
Dianqiang Li Pei Cheng Shuping He 《Mathematical Methods in the Applied Sciences》2017,40(11):4197-4210
In this paper, we aim to investigate the exponential stability of general hybrid stochastic functional differential systems with delayed impulses. By using the average impulsive interval and the Lyapunov function method, we derive some sufficient conditions for exponential stability, which are less conservative than those existing results based on the supremum or infimum of impulsive interval and more convenient to be applied than those Razumikhin‐type conditions in the literature. Meanwhile, we show that unstable hybrid stochastic delay differential systems, both linear and nonlinear, can be stabilized by suitably impulsive sequence. Finally, two examples are discussed to illustrate the effectiveness and advantages of the obtained results. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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Qi Luo 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e487
The Lyapunov direct method, as the most effective measure of studying stability theory for ordinary differential systems and stochastic ordinary differential systems, has not been generalized to research concerning stochastic partial differential systems owing to the emptiness of the corresponding Ito differential formula. The goal of this paper is just employing the Lyapunov direct method to investigate the stability of Ito stochastic reaction diffusion systems, including asymptotical stability in probability and almost sure exponential stability. The obtained results extend the conclusions of [X.X. Liao, X.R. Mao, Exponential stability and instability of stochastic neural networks, Stochastic Analysis and Applications 14 (2) (1996) 165-185; X.X. Liao, S.Z. Yang, S.J. Cheng, Y.L. Fu, Stability of general neural networks with reaction-diffusion, Science in China (F) 44 (5) (2001) 389-395]. 相似文献
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Tomás CaraballoJosé A. Langa Takeshi Taniguchi 《Journal of Differential Equations》2002,179(2):714-737
Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier-Stokes equation are established. The first ones are proved as a consequence of the exponential mean square stability of the solutions. However, some of them are improved by avoiding the previous mean square stability in some more particular and restrictive situations. Also, some results and comments concerning the stabilizability and stabilization of these equations are stated. 相似文献