一类状态依赖时滞的广义时滞微分系统稳定性判据

主要讨论了一类退化时滞微分系统的德定性问题.退化时滞微分系统稳定性的研究与非奇异系统或不带时滞的退化系统的稳定性研究均有不同.为了解决所遇到的困难,提出一种判定退化时滞微分系统稳定性的新判据.首先利用可逆的线性变换将系统转化为线性中立型微分系统,然后利用线性矩阵不等式以及构造Lyapunov函数,通过讨论这类线性中立型...     

变时滞分布参数系统的全局指数稳定性

基于比较原理,利用推广的向量Hanalay微分不等式,Dini导数,结合Green公式及不等式分析技术,研究几类变时滞分布参数控制系统所导出的滑动模运动方程的全局指数稳定性问题,在仅要求系数矩阵是个M-矩阵的条件下,获得了几类滑动模运动方程全局指数稳定性的充分条件,建立了滑动模运动方程全局指数稳定性定理.推广和改进了前人的结论.并为研究时滞分布参数系统的变结构控制问题奠定了基础.     

基于LMI的混合时滞随机神经网络指数稳定性

为研究具有混合时滞的随机反馈神经网络的平衡解的稳定性问题,基于Lyapunov稳定性理论及It随机微分公式计算了随机神经网络得到在均方意义下的全局指数稳定性.利用网络模型中混合时滞的形式特点构造了新型的Lyapunov-Krasovskii泛函,并借助矩阵不等式分析技巧建立了新型采用线性矩阵不等式形式的判别条件,较已有采用矩阵范数形式的判别条件放宽了要求.线性矩阵不等式可以利用Matlab中提供的线性矩阵不等式进行计算验证,使得所得判别条件更加实用.最后给出了数值证明判别条件的有效性.     

一类变时滞中立型系统的全局指数稳定性研究

利用Lyapunov方法对变时滞的线性中立型微分系统的全局指数稳定性进行分析,并估计其指数收敛率,得到了两个实用的全局指数稳定性判据。这些稳定判据都表示为线性矩阵不等式（LMI）形式,易于验证。数字仿真实例验证了所得结果的有效性。     

不确定随机离散分布时滞神经网络的鲁棒稳定性*

采用Its微分公式和不等式分析技巧,研究了一类不确定随机离散分布时滞神经网络的鲁棒稳定性问题。该模型同时考虑了神经网络模型的两种扰动因素,即随机扰动与不确定性扰动。通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了系统在均方根意义下的全局鲁棒稳定性判据,能够利用LMI工具箱很容易地进行检验。此外,仿真结果进一步证明了结论的有效性。     

具有状态时滞的Markov切换系统的指数稳定性新结果

考虑具有状态时滞的Markov切换系统的均方指数稳定性分析问题. 为此, 我们构造了一类较为一般的与模态相关的Lyapunov-Krasovskii泛函, 并利用Markonv过程的统计性质计算泛函的微分. 进而, 通过引入自由权矩阵建立了以线性矩阵不等式表述的稳定性准则. 仿真算例验证了方法的有效性.     

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.     

区间时滞神经网络的随机稳定性

分析了区间变时滞的随机神经网络的全局渐进稳定性。区间变时滞不仅考虑了时变因素,而且考虑了时滞时变的上界和下界。通过Itô’s 微分公式和构造适当的李雅普罗夫泛函,并且引入自由权值矩阵,以线性矩阵不等式形式给出了该系统在均方意义下的全局渐进稳定的充分性判据。数值算例进一步证明了结论的有效性。     

多时变状态和控制时滞系统的绝对稳定性

研究了具有多时变状态和控制时滞的Lurie控制系统基于线性矩阵不等式(LMI)的绝对稳定性条件.首先,构造了关于Lyapunov泛函中正定矩阵和积分项系数等自由参数的LMI,获得了系统时滞无关绝对稳定条件.进一步引入自由权矩阵来表示牛顿-莱布尼兹公式中各项的相互关系,得到了系统绝对稳定的时滞相关条件.最后,通过一个实例阐述了本文方法的有效性和相比已有结果的优越性.     

中立型变时滞系统的鲁棒稳定性

考虑不确定中立型变时滞系统的鲁棒稳定性问题. 首先, 引入新的变量来代替系统的不确定性; 然后, 通过构造一般形式的Lyapunov-Krasovskii泛函、使用积分不等式并引入自由矩阵, 得到了基于线性矩阵不等式的系统稳定性判据. 该结论与中立型时滞, 离散时滞及其导数均相关, 具有较小的保守性. 最后, 通过仿真算例说明了所得到的结论在保守性上优于现存的结果以及中立型时滞, 离散时滞及其导数三者之间的关系.     

Exponential stability of a class of impulsive stochastic delay partial differential equations driven by a fractional Brownian motion

Several new criteria on exponential stability of a class of impulsive stochastic delay partial differential equations with a fractional Brownian motion are presented by employing the variation of parameters formula and using an inequality technique. The criteria we provided in this paper do not assume the condition that the corresponding continuous stochastic system is stable, so this criteria can be applied to stabilize unstable systems. Moreover, the exponential convergence rate is estimated. Some examples are given to illustrate our main results.     

Stochastically exponential stability and stabilization of uncertain linear hyperbolic PDE systems with Markov jumping parameters

This paper is concerned with the problem of robustly stochastically exponential stability and stabilization for a class of distributed parameter systems described by uncertain linear first-order hyperbolic partial differential equations (FOHPDEs) with Markov jumping parameters, for which the manipulated input is distributed in space. Based on an integral-type stochastic Lyapunov functional (ISLF), the sufficient condition of robustly stochastically exponential stability with a given decay rate is first derived in terms of spatial differential linear matrix inequalities (SDLMIs). Then, an SDLMI approach to the design of robust stabilizing controllers via state feedback is developed from the resulting stability condition. Furthermore, using the finite difference method and the standard linear matrix inequality (LMI) optimization techniques, recursive LMI algorithms for solving the SDLMIs in the analysis and synthesis are provided. Finally, a simulation example is given to demonstrate the effectiveness of the developed design method.     

Delay-dependent exponential stability of the backward Euler method for nonlinear stochastic delay differential equations

Recently, several scholars discussed the question of under what conditions numerical solutions can reproduce exponential stability of exact solutions to stochastic delay differential equations, and some delay-independent stability criteria were obtained. This paper is concerned with delay-dependent stability of numerical solutions. Under a delay-dependent condition for the stability of the exact solution, it is proved that the backward Euler method is mean-square exponentially stable for all positive stepsizes. Numerical experiments are given to confirm the theoretical results.     

Impulses-induced p-exponential input-to-state stability for a class of stochastic delayed partial differential equations

This paper proposes a new stability concept called p-exponential input-to-state stability (pISS) for impulsive stochastic delayed partial differential equations (ISDPDEs). By employing the formula for the variation of parameters, the average impulsive interval approach and a new impulsive integral inequality, the sufficient conditions for pISS of ISDPDEs are derived. The issue of impulsive stabilisation to pISS of ISDPDEs is studied. It is unveiled that if the continuous stochastic delay partial differential equations may not be pISS, it can be stabilised by impulsive control. An example is given to illustrate our main results.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

Mean-square exponential stability of impulsive stochastic time-delay systems with delayed impulse effects

This paper is concerned with the mean-square exponential stability problem for a class of impulsive stochastic systems with delayed impulses. The delays exhibit in both continuous subsystem and discrete subsystem. By constructing piecewise time-varying Lyapunov functions and Razumikhin technique, sufficient conditions are derived which guarantee the mean-square exponential stability for impulsive stochastic delay system. It is shown that the obtained stability conditions depend both on the lower bound and the upper bound of impulsive intervals, and the stability of system is robust with regard to sufficiently small impulse input delays. Finally, two examples are proposed to verify the efficiency of the proposed results.     

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.     

Input delay compensation of nonlinear stochastic systems with both state and input delays by prediction approach

In this study, we present an extension of the prediction scheme (dynamic control) for nonlinear stochastic systems with both input and state delays. The stochastic system includes multiplicative noise and it is modelled as Ito stochastic differential equation. Input delay is considered to be equal or less than state delay and both delays are considered to be constant. At first, a new formula for prediction of the system's state is presented and then by means of this prediction vector, control input is constructed. To calculate the stabilising gain of the predictive controller, some sufficient delay-independent conditions in the form of linear matrix inequality are presented. Finally, simulation examples are given to illustrate the effectiveness of the proposed approach.     

具分布参数的随机Hopfield神经网络的指数稳定

基于随机Fubini定理,将随机偏微分方程描述的Hopfield神经网络系统转化为用相应的随机常微分方程来描述.利用关于空间变量平均的Lyapunov函数与Ito^公式,通过对所构造的Lyapunov函数在Ito^微分规则下对相应系统求导的方法,获得了系统指数稳定的代数判据及其Lyapunov指数估计.实现了运用Lyapunov直接法对分布参数系统稳定性的研究.     

Consensus of nonlinear multiagent systems with mode-dependent delay via stochastic sampled data under Markovian switching topologies

In this article, we investigate the mean-square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time-varying delay switch randomly which are regulated by a time-homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean-square consensus. For the undirected topology case, a low-dimensional LMI-based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.