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1.
随机时变线性系统的稳定性   总被引:1,自引:0,他引:1  
潘继斌 《数学研究》2000,33(2):157-162
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
2.
In this paper, we investigate exponential stability for stochastic BAM networks with mixed delays. The mixed delays include discrete and distributed time-delays. The purpose of this paper is to establish some criteria to ensure the delayed stochastic BAM neural networks are exponential stable in the mean square. A sufficient condition is established by consructing suitable Lyapunov functionals. The condition is expressed in terms of the feasibility to a couple LMIs. Therefore, the exponential stability of the stochastic BAM networks with discrete and distributed delays can be easily checked by using the numerically efficient Matlab LMI toobox. A simple example is given to demonstrate the usefulness of the derived LMI-based stability conditions.  相似文献
3.
This paper studies the problems of global exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays. By employing a new Lyapunov-Krasovskii functional and linear matrix inequality, some criteria of global exponential stability in the mean square for the reaction-diffusion high-order neural networks are established, which are easily verifiable and have a wider adaptive. An example is also discussed to illustrate our results.  相似文献
4.
In this paper, we consider a class of stochastic neutral partial functional differential equations in a real separable Hilbert space. Some conditions on the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths are obtained. The known results in Govindan [T.E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77 (2005) 139-154], Liu and Truman [K. Liu, A. Truman, A note on almost sure exponential stability for stochastic partial functional differential equations, Statist. Probab. Lett. 50 (2000) 273-278] and Taniguchi [T. Taniguchi, Almost sure exponential stability for stochastic partial functional differential equations, Stoch. Anal. Appl. 16 (1998) 965-975; T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics 53 (1995) 41-52] are generalized and improved.  相似文献
5.
研究一类不确定随机时滞系统的时滞相关鲁棒镇定问题.通过引入参数化的中立型模型变换,构造Lyapunov-krasovskii泛函,运用线性矩阵不等式方法,得到了使得闭环系统为均方指数稳定的保守性较小的时滞相关鲁棒镇定条件.  相似文献
6.
本文研究一类具有分离变量的非线性随机不确定系统的稳定性问题。采用线性矩阵不等式(LMI)和Lyapunov—Krasovskii泛函的方法,获得了局部指数稳定性的时滞盯关性判据。仿真结果证明了结论的可行性和优越性。  相似文献
7.
该文通过系统变换技巧, 构造出新型的Lyapunov泛函. 利用此Lyapunov泛函, 基于线性矩阵不等式, 得到了随机Hopfield时滞神经网络与时滞相关及与时滞无关均方指数稳定性新的充分条件. 数值例子表明, 与已有结果相比, 该文的结果具有较少的保守性.  相似文献
8.
该文基于随机线性二次控制问题, 讨论了多时滞、且具有马尔可夫跳变参数的微分系统的最优控制的鲁棒性及可镇定问题.应用了Lyapunov-Krasovskii型的泛函、伊藤(Ito)公式、及Schur补等工具, 分析了该随机多时滞、具有马尔可夫过程的微分系统的均方指数稳定性.得到了时滞相关与时滞无关的充分性的代数判据.  相似文献
9.
 本文首先研究了一维带跳随机微分方程的指数稳定性,并证明 Euler-Maruyama (EM)方法保持了解析解的稳定性.其次,研究了多维带跳随机微分方程的稳定性,证明若系数满足全局Lipchitz条件,则 EM 方法能够很好地保持解析解的几乎处处指数稳定性、均方指数稳定性. 最后,给出算例来支持所得结论的正确性.  相似文献
10.
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