基于均方指数稳定的随机时延网络系统的输出反馈控制

研究了随机时延网络系统的输出反馈控制问题.通过把网络诱导时延和数据丢包看做满足区间Bernoulli分布的等价时延,建立了随机时延网络系统模型.基于随机系统稳定性理论,以线性矩阵不等式形式给出了系统均方指数稳定条件和输出反馈控制器设计方法.仿真结果说明了该方法的有效性.     

中立型带跳不确定变时滞随机系统鲁棒指数稳定

研究了一类中立型Markov跳变随机系统鲁棒指数稳定性,借助于Lyapunov-Krasovskii 泛函方法和随机稳定性理论,给出并证明了使中立型Markov跳变时滞随机系统指数稳定的充分条件,所有结果以线性矩阵不等式形式给出,算例表明了所给出的稳定性判据的有效性.     

Markov切换扩散过程的几乎处处渐近稳定性

本文研究一类Markov切换扩散过程的样本轨道长时间行为,分几类情形讨论其几乎处处渐近稳定性.对于Markov链状态空间是有限的这类过程的稳定性,应用Perron-Frobenius定理证明;对于可逆的Markov链且其状态空间是有限的这类过程的稳定性,应用主特征值方法证明;对于Markov链状态空间是可数的这类过程的稳定性,应用有限划分技巧及M-矩阵方法证明.每一种情形,相应的例子给出了说明.进一步,使用得到的理论,对线性Markov切换扩散过程的反馈控制问题进行讨论.     

基于观测器的模糊时滞系统的指数稳定控制

研究一类模糊时滞系统的指数稳定和基于观测器的模糊控制问题.在系统状态未知的情况下,通过设计系统的模糊观测器利用矩阵不等式分析的方法给出了系统指数稳定条件和基于观测器的动态输出反馈控制器设计方案.仿真结果说明了所提方法的有效性.     

时滞不确定性Markov切换线性随机微分系统的指数鲁棒稳定性

研究了一类时滞不确定性Markov切换随机微分系统的均方指数鲁棒随机稳定性\bd 系统中的时滞是时变的, 不确定项结构为范数有界, Markov切换是连续时间、离散状态的时齐Markov过程{\bf\!.} 利用随机Lyapunov函数方法和LMI技术, 得到了几个判定系统均方指数鲁棒随机稳定性的充分性条件\bd 一个数值例子说明了判据的有效性和可行性.     

确定环形Markov链的Q-矩阵

给出了Markov链中任一状态集的逗留时间或击中时间的分布(混合指数分布),以及其分布的各阶微分与Q-矩阵之间的约束方程组.利用该约束关系及环形链结构的先验信息,采用Markov链反演方法证明了:对于有限状态环形Markov链,其Q-矩阵能由其中任意两个相邻状态的逗留时间和击中时间分布唯一决定,并给出了相应的算法.     

Markov链在生态学中的一个应用

Markov链是随机过程的一个特例,专门研究在无后效条件下时间和状态均为离散的随机转移问题.本文运用与Markov链相关的转移概率矩阵性质,探讨一个鱼类洄游实际问题的数学模型,寻求鱼类洄游的数量规律.     

网络环境下的大系统鲁棒H_∞控制

针对网络环境下的一类同时具有测量数据和控制数据丢失的线性离散大系统,研究其H_∞状态反馈控制器设计问题.大系统由N个线性离散关联子系统构成,假设测量数据和控制数据丢失满足已知概率的Bernoulli分布,采用线性矩阵不等式方法给出了H_∞控制器存在的充分条件,所设计的控制器使得闭环系统均方指数稳定且满足指定的H_∞性能指标.最后通过仿真例子说明该方法的有效性.     

非线性中立型随机微分系统的稳定性

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.     

不同元件构成系统中元件维修率分布确定

将Markov链引入SFT理论中,计算可表示环境因素影响的元件维修率分布.研究针对不同元件构成的串联、并联和混联系统中元件的维修率分布计算方法.给出了串联和并联系统中元件维修率推导过程.对状态转移概率的计算不使用Markov状态转移矩阵求解,而是根据Markov状态转移图中的状态关系求解.使用SFT中的元件故障概率分布代替Markov链中的失效率,可得到元件维修率分布.以混联系统作为实例进行分析,使用状态关系求解各状态转移概率关系,得到了3个元件在使用时间t和使用温度c影响下的维修率分布,及正常状态转移概率范围.     

Robust exponential stability analysis for stochastic genetic networks with uncertain parameters

In this paper, the robust exponential stability problem is considered for a class of stochastic genetic networks with uncertain parameters. Under assumptions that the parameter uncertainties are norm bounded, both cases that the genetic network has or has not time delays are discussed. Sufficient conditions are derived to guarantee the robust exponential stability in the mean square of stochastic genetic networks for all admissible parameter uncertainties. By applying Lyapunov function (functional) and conducting some stochastic analysis, the stability criteria are given in the form of linear matrix inequalities (LMI’s), which can be easily checked in practice. Two illustrative examples are also given to show the usefulness of the proposed criteria.     

分段连续型随机微分方程指数Euler方法的稳定性

给出了线性分段连续型随机微分方程指数Euler方法的均方指数稳定性.经典的对稳定性理论分析,通常应用的是Lyapunov泛函理论,然而,应用该方程本身的特点和矩阵范数的定义给出了该方程精确解的均方稳定性.以往对于该方程应用隐式Euler方法得到对于任意步长数值解的均方稳定性,而应用显式Euler方法得到了相同的结果.最后,给出实例验证结论的有效性.     

Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-structured population system with diffusion. The definition of exponential mean square stability of numerical method is introduced. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

一类随机BAM细胞神经网络的指数稳定性

研究了一类随机BAM细胞神经网络的指数稳定性,利用Lyapunov函数理论、It公式和线性矩阵不等式方法,建立了这种细胞神经网络均方指数稳定性判定的充分性条件.     

具有时滞的奇异扰动随机微分方程的均方指数稳定性

本文利用常数变易公式,随机过程数学期望的性质,矩阵范数,测度的相关理论以及不等式技巧,对一类具有时滞的奇异扰动随机微分方程的均方指数稳定性进行了讨论,得到了该类方程均方指数稳定的充分条件的代数判据.     

Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays

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.     

Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays

Convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov functional method, M-matrix properties, some inequality technique and nonnegative semimartingale convergence theorem are used in our approach. These criteria ensuring the different exponential stability show that diffusion and delays are harmless, but random fluctuations are important, in the stochastic continuously distributed delayed reaction–diffusion RNNs with the structure satisfying the criteria. Two examples are also given to demonstrate our results.     

Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses

In this paper, the problem of stability analysis for a class of delayed stochastic bidirectional associative memory neural network with Markovian jumping parameters and impulses are being investigated. The jumping parameters assumed here are continuous-time, discrete-state homogeneous Markov chain and the delays are time-variant. Some novel criteria for exponential stability in the mean square are obtained by using a Lyapunov function, Ito’s formula and linear matrix inequality optimization approach. The derived conditions are presented in terms of linear matrix inequalities. The estimate of the exponential convergence rate is also given, which depends on the system parameters and impulsive disturbed intension. In addition, a numerical example is given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.     

基于LMI方法的多时滞随机神经网络的指数稳定性

研究了一类具有多个时滞的随机神经网络的均方指数稳定性问题,应用Lyapunov-Krasovskii泛函稳定理论和线性矩阵不等式(LMI)方法,建立了该系统解的指数稳定判别准则,最后通过数值举例阐述了结果的有效性.