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。     

多滞后线性随机系统的稳定性判据

本文利用作者建立的时滞随机系统的比较原理和多滞后确定性系统的稳定性结论，建立了多滞后线性随机系统的滞后无关均方渐近稳定性的判据。     

时变滞后随机大系统的稳定性：向量Lyapunov函数法

本文研究变系数、变时滞线性随机大系统的均方渐近稳定性，通过将Ｈａｌａｎａｙ不等式推广到高维空间、采用向量Ｌｙａｐｕｎｏｖ函数、运用Ｍ－矩阵等工具，得到了随机大系统的稳定性判据，文中模型考虑了子系统之间的交互随机干扰，所得稳定性判断是滞后无关的。     

带有时滞的随机大系统的稳定性

本文对带有时滞的随机大系统给出了滞后无关均方渐近稳定性的定义和判据,所讨论的随机大系统具有随机互联结构。     

具有滞后耦合特性的线性随机大系统的时滞无关均方稳定性

本文研究具有滞后耦合特性的时不变线性Ｉｔｏ随机大系统的稳定性，得到了大系统平衡态滞后无关的均方渐近稳定性代数判据。文中所考虑的子系统是随机子系统，对它们的建设正好是它们的均方渐近稳定的充要条件。另外，文中采用的Ｌｙａｐｕｎｏｖ泛函是确定型的Ｌｙａｐｕｎｏｖ泛函。     

具有滞后耦合特性的线性随机大系统的时滞无关均方稳定性*

本文研究具有滞后耦合特性的时不变线性Ｉｔｏ随机大系统的稳定性，得到了大系统平衡态滞后无关的均方渐近稳定性代数判据．文中所考虑的子系统是随机子系统，对它们的假设正好是它们均方渐近稳定的充要条件．另外，文中采用的Ｌｙａｐｕｎｏｖ泛函是确定型的Ｌｙａｐｕｎｏｖ泛函．     

完全滞后系统的滞后反馈镇定

研究完全滞后系统的滞后状态反馈镇定.通过建立关于时滞系统的新型渐近稳定性定 理.构造适当的Lyapunov泛函、利用矩阵Riccati代数方程,得到了完全滞后系统的滞后反 馈镇定方法.     

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。     

线性时滞系统滞后反馈鲁棒镇定

本文研究时不变线性时滞系统的鲁棒镇定问题。通过建立时滞系统的一个渐近稳定性定理，对摄动矩阵满足匹配条件和不满足匹配条件的情况分别给出了完全鲁棒镇定控制器的设计方法与鲁棒镇定控制器的存在性充分条件和设计方法；文中尤其提出了非滞后线性系统的一种简单的滞后反馈镇定方案。文末用例子示例了本文的设计方法。     

时滞非线性随机大系统的指数稳定性

建立了一般随机泛函微分方程p阶均值指数稳定与几乎必然指数稳定的新型判据, 然后应用所得判据到具有可变多时滞的非线性随机大系统, 得到了这种随机大系统时滞无关的均方指数稳定与几乎必然指数稳定的代数判据.     

具有非线性滞后关联的随机大系统的分散镇定

本文通过利用李雅普诺夫函数和李雅普诺夫矩阵方程的性质，对具有非线性滞后关联的一类随机大系统建立了分散鲁棒镇定的判据，所得闭环随机大系统的和稳定性不依赖于任意实数滞后，并对不确定系数矩阵和随机扰动强度具有鲁棒性。     

非线性随机时滞系统的稳定性与应用

首先考虑了不确定性的一族非线笥随机时滞系统,建立了这种系统的均方指数稳定与几乎必须指数稳定的充分准则,其准则是时滞无关的,然后应用这些充分条件到一类不确定的随机时滞神经网络,得到了这咱神经网络指数稳定的产用判据。本文的结果是最近文献中某些结果的推广,最后一个数值例子说明的所给准则的有效性。     

灰色随机线性时滞系统的渐近稳定性

首先提出了灰色随机线性时滞系统及其渐近稳定性的概念;然后,利用矩阵理论和随机微分时滞方程解的渐近收敛定理及李雅普诺夫函数,研究了灰色随机线性时滞系统的渐近稳定性,得到了随机淅近稳定的几个充分性条件;最后,通过数值例子说明了所得结果在实际应用中的方便性和有效性.     

Stabilization of Stochastic Coupled Systems With Time Delay Via Feedback Control Based on Discrete‐Time State Observations

In this paper, the stabilization of stochastic coupled systems (SCSs) with time delay via feedback control based on discrete‐time state observations is investigated. We use the discrete‐time state feedback control to stabilize stochastic coupled systems with time delay. Moreover, by employing Lyapunov method and graph theory, the upper bound of the duration between two consecutive state observations is obtained and some criteria are established to guarantee the stabilization in sense of ‐stability and mean‐square asymptotic stability of SCSs with time delay via feedback control based on discrete‐time state observations. In addition, to verify the theoretical results, stochastic coupled oscillators with time delay are performed. At last, a numerical example is given to illustrate the applicability and effectiveness of our analytical results.     

Generalized criteria on delay‐dependent stability of highly nonlinear hybrid stochastic systems

Our recent paper (Fei W, etal. Delay dependent stability of highly nonlinear hybrid stochastic systems. Automatica. 2017;82:165‐170) is the first to establish delay‐dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear, we mean that the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper. We will then develop our ideas and methods there to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs.     

具有多状态滞后的不确定时变时滞系统的鲁棒镇定

首先给出了具有多状态滞后的时变时滞系统渐近稳定的代数Riccati不等式形式的判据, 并基于此给出了确定性时变时滞系统的镇定方法.然后给出了具有有界参数不确定性的多状态滞 后时变时滞系统的镇定方法.文中的结论非常简单,只需解一个代数Riccati方程.最后给出一个算 例.     

An analysis of the exponential stability of linear stochastic neutral delay systems

This paper is concerned with the analysis of the mean square exponential stability and the almost sure exponential stability of linear stochastic neutral delay systems. A general stability result on the mean square and almost sure exponential stability of such systems is established. Based on this stability result, the delay partitioning technique is adopted to obtain a delay‐dependent stability condition in terms of linear matrix inequalities (LMIs). In obtaining these LMIs, some basic rules of the Ito calculus are also utilized to introduce slack matrices so as to further reduce conservatism. Some numerical examples borrowed from the literature are used to show that, as the number of the partitioning intervals increases, the allowable delay determined by the proposed LMI condition approaches h_max, the maximal allowable delay for the stability of the considered system, indicating the effectiveness of the proposed stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term

Global asymptotic stability conditions for discrete vector nonlinear stochastic systems with state delay and Volterra diffusion term are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The derived stability conditions are directly expressed in terms of the system coefficients. A number of nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given. The obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems.