随机控制系统Euler-Maruyama方法的均方指数输入状态稳定性

分析了随机控制系统Euler-Maruyama (EM)方法的均方指数输入状态稳定性. 本文的目的是寻找随机控制系统和EM方法分享它们均方指数输入状态稳定性的条件. 在全局Lipschitz系数和均方连续随机输入的基础上, 二阶矩的界和合适形式的强收敛条件被得到了. 在该强收敛条件下, 我们证明了一个随机控制系统是均方指数输入状态稳定的, 当且仅当对充分小的步长, EM方法也是均方指数输入状态稳定的.     

具有漏泄时滞的随机神经网络的均方指数稳定性

在实现复杂的人工神经网络模型的过程中,随机噪声是不可避免的。建立具有随机噪声干扰的神经网络模型不但是设计上的需要,而且能够更加真实地反映生物神经网络的特点。本文利用构造合适的Lyapunov泛函,应用It?微分公式及Jensen不等式性质等,研究了一类具有漏泄时滞的随机神经网络的动力学行为,得到了确保该系统均方指数稳定的充分判别条件。最后, 通过两个数值计算的例子,说明所得结论的有效性。     

不确定变时滞随机系统的鲁棒均方指数稳定性

研究了不确定变时滞随机系统的鲁棒均方指数稳定性问题, 不确定性是范数有界的. 通过构造Lyapunov泛函, 得到了基于线性矩阵不等式的鲁棒均方指数稳定的充分条件. 最后给出实例加以验证所提出方法的有效性.     

分布时滞随机偏微分系统的均方指数稳定性

针对一类同时具有分布时滞和维纳过程的随机偏微分系统, 首先基于It?o微分公式, 通过计算弱无穷小算子, 得到了随机微分导数; 其次利用Green公式和积分不等式及Schur补引理对矩阵不等式进行处理; 然后对微分两边积分并同时取数学期望处理随机交叉项; 获得了分布时滞随机偏微分系统是均方指数稳定的充分条件. 在此基础上, 进一步考虑了离散变时滞和分布变时滞在一定约束情形下的分布时滞随机偏微分系统的均方指数稳定性问题.最后给出仿真实例, 仿真结果表明所获得的线性矩阵不等式条件保证了系统的稳定性, 验证了所得结论的有效性.     

随机延迟积分微分方程改进分步向后Euler方法的均方指数稳定性

本文研究一类改进分步向后Euler方法求解随机延迟积分微分方程的均方指数稳定性．证明了在约束网格下,该方法依步长h=τ／m保持原系统的均方指数稳定性．数值试验验证了本文理论结果的正确性．     

非线性滞后Ito随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ｉｔｏ随机系统的滞后无关均方渐近稳定性，将关于线性时滞不等式的Ｈａｌａｎａｙ不等式推广到非线性情形，用Ｌｙａｐｕｎｏｖ函数和关于时滞随机系统的比较原理，得到了非线性滞后Ｉｔｏ随机系统滞后无关均方渐近稳定性的一些判据。     

时滞线性随机系统的均方稳定性与反馈镇定*

本文研究Ｉｔｏｏ型随机滞后系统的均方稳定性与反馈镇定。文中首先建立了Ｉｔｏ型随机滞后系统的新型稳定性定理,然后采用适当的Ｌｙａｐｕｎｏｖ泛函得到了时滞线性随机系统零解均方渐近稳定的一个充分性判据,该判据适用于完全滞后型的随机系统,据此判据,文中给出了时滞线性随机系统的滞后反馈镇定方法。     

随机细胞神经网络平衡点均方指数稳定性分析

主要利用Lyapunov 泛函方法研究带脉冲的随机时滞神经网络平衡点的均方指数稳定性。主要借助于不等式,随机分析理论给出主要结果。最后给出一数值算例证明结果的有效性。     

非线性控制系统的输入-状态稳定性及有关问题

输入-状态稳定性是80年代末对非线性控制系统提出的一个有用的概念,由于其具有广泛的应用前景,而得到普遍的重视,本文介绍进入90年代以来对这种稳定性以及由此派生出来的其他稳定性研究的主要成果,讨论了相关的镇定问题,同时给出作者的评注。     

时延网络控制系统的方指数稳定的研究

针对网络控制系统中普遍存在的时间延迟,采用事件驱动方式对系统进行建模,并针对该数字模型提出了使系统达到均方指数稳定的控制律设计方法,仿真结果表明了所提出方法的有效性。     

Exponential mean-square stability of the θ-method for neutral stochastic delay differential equations with jumps

The exponential mean-square stability of the θ-method for neutral stochastic delay differential equations (NSDDEs) with jumps is considered. With some monotone conditions, the trivial solution of the equation is proved to be exponentially mean-square stable. If the drift coefficient and the parameters satisfy more strengthened conditions, for the constrained stepsize, it is shown that the θ-method can preserve the exponential mean-square stability of the trivial solution for θ ∈ [0, 1]. Since θ-method covers the commonly used Euler–Maruyama (EM) method and the backward Euler–Maruyama (BEM) method, the results are valid for the above two methods. Moreover, they can adapt to the NSDDEs and the stochastic delay differential equations (SDDEs) with jumps. Finally, a numerical example illustrates the effectiveness of the theoretical results.     

Choice of θ and its effects on stability in the stochastic θ-method of stochastic delay differential equations

The second author's work [F. Wu, X. Mao, and L. Szpruch, Almost sure exponential stability of numerical solutions for stochastic delay differential equations, Numer. Math. 115 (2010), pp. 681–697] and Mao's papers [D.J. Higham, X. Mao, and C. Yuan, Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations, SIAM J. Numer. Anal. 45 (2007), pp. 592–607; X. Mao, Y. Shen, and G. Alison, Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations, J. Comput. Appl. Math. 235 (2011), pp. 1213–1226] showed that the backward Euler–Maruyama (BEM) method may reproduce the almost sure stability of stochastic differential equations (SDEs) without the linear growth condition of the drift coefficient and the counterexample shows that the Euler–Maruyama (EM) method cannot. Since the stochastic θ-method is more general than the BEM and EM methods, it is very interesting to examine the interval in which the stochastic θ-method can capture the stability of exact solutions of SDEs. Without the linear growth condition of the drift term, this paper concludes that the stochastic θ-method can capture the stability for θ∈(1/2, 1]. For θ∈[0, 1/2), a counterexample shows that the stochastic θ-method cannot reproduce the stability of the exact solution. Finally, two examples are given to illustrate our conclusions.     

混杂随机微分方程θ方法的几乎必然指数稳定性

大部分的混杂随机微分方程很难得到解析解, 因此利用数值方法研究其数值解具有重要意义. 本文研究θ方法产生的数值解的几乎必然指数稳定性. 在单边Lipschitz条件和线性增长条件下, 首先给出方程的平凡解是几乎必然指数稳定的. 然后在相同条件下, 运用Chebyshev不等式和Borel-Cantelli引理, 证明了对θ ∈ [0,1], θ方法重现平凡解的几乎必然指数稳定性. θ方法是一种比现有的Euler-Maruyama方法和向后Euler-Maruyama方法更广的方法. 当θ等于1或0时,它分别退化为上述两种方法之一. 本文的结论对上述两种方法同样适用. 最后, 数值例子和仿真说明了对不同的θ所提出方法的有效性和稳定性.     

Sliding mode control of switched hybrid systems with stochastic perturbation

This paper is concerned with the sliding mode control (SMC) of a continuous-time switched stochastic system. A sufficient condition for the existence of reduced-order sliding mode dynamics is derived and an explicit parametrization of the desired sliding surface is also given. Then, a sliding mode controller is then synthesized for reaching motion. Moreover, the observer-based SMC problem is also investigated. Some sufficient conditions are established for the existence and the solvability of the desired observer and the observer-based sliding mode controller is synthesized. Finally, numerical examples are provided to illustrate the effectiveness of the proposed theory.     

A new result on stability analysis for stochastic neutral systems

This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results.     

Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control

In this paper we are concerned with the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations (also known as stochastic differential equations with the Markovian switching) by discrete-time feedback controls. Although the stabilization by continuous-time feedback controls for such equations has been discussed by several authors (see e.g. , , ,  and ), there is so far no result on the stabilization by discrete-time feedback controls. Our aim here is to initiate the study in this area by establishing some new results.