Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters: a delay decomposition approach

The mean-square exponential stability problem is investigated for a class of stochastic time-varying delay systems with Markovian jumping parameters.By decomposing the delay interval into multiple equidistant subintervals,a new delay-dependent and decay-rate-dependent criterion is presented based on constructing a novel Lyapunov functional and employing stochastic analysis technique.Besides,the decay rate has no conventional constraint and can be selected according to different practical conditions.Finally,two numerical examples are provided to show that the obtained result has less conservatism than some existing ones in the literature.     

不确定随机跳变时滞系统非脆弱H∞滤

针对一类具有马尔可夫跳变参数的It^o类型不确定随机时滞系统,讨论了该类系统的鲁棒非脆弱H_∞滤波问题。在被控对象及滤波器同时存在不确定性的情况下,闭环滤波误差系统渐近稳定,干扰抑制性能指标小于给定上界。通过构造一个Lyapunov Krasovskii泛函,应用It^o微分公式沿系统对其求微分,再运用线性矩阵不等式（linear matrix inequality, LMI）和It^o公式,给出了非脆弱滤波器存在的可解性条件。通过数值算例表明了该方法的有效性。     

On passivity of state delayed stochastic jump systems

1.INTRODUCTION Stochasticjumpsystemisaspecialkindofhybridsys tems.Itisdescribedbyacontinuous timefinite state Markovprocesswhichreferstothemode,andbya dynamicsystemofdifferentialequationswhichrefers tothestate.Thejumpsystemscanmodelthedynam icsystemssubjecttoabruptvariationintheirstruc turesandthereforattractresearchinterestinginthe world.Recently,thereweresomeresearchesoncon trolproblemsforjumpsystemswithtimedelay[1,2].Passivityplaysanimportantroleinsystemand controltheory.Butalmostallr…     

Stability of stochastic neural networks with Markovian jumping parameters

The global asymptotical stability for a class of stochastic delayed neural networks (SDNNs) with new delay-dependent stability conditions are derived. All results are expressed in terms of linear matrix inequality (LMI), and a numerical example is presented to illustrate the correctness and less conservativeness of the proposed method.     

H∞ control for stochastic systems with time-delay

The H∞-control problem of stochastic systems with time-delay is considered. The sufficient conditions are obtained, under which there are always state-feedback control and dynamic output-feedback control so that the resulting closed-loop system is internaly stable and L2 input-output stable in the sense of expectation. Furthermore, the explicit formulas of both kinds of controls are derived. An example is included to illustrate the correctness of theoretic results.     

一类逻辑环随机模型的队列与站点状态转移

借助随机服务系统理论,探讨带有优先队列逻辑环随机模型的状态转移有关问题,主要内容有：(1)阐述系统和站点队列排队服务模型及特点;(2)描绘队列状态转移图,提出队列状态零转移和非零转移问题;(3)给出判断队列状态转移性质的条件;(4)导出队列和站点(双队列)状态转移概率算法;(5)引出队列和站点的无条件零转移概念。通过相关数学表达式和典型事例等,表征该系统队列和站点所具有的状态转移特性。     

Robust dissipative control for time-delay stochastic jump systems

A robust dissipative control problem for a class of It?-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent (RSSWDD) and strictly (Q, S, R)-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality (LMI). And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay.Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors,few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems.Firstly,the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem.Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities.In particular,the estimate of the exponential convergence rate is also provided,which depends on system parameters and impulsive effects.The obtained results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows,and impulses may be used as controllers to stabilize the underlying stochastic system.Numerical examples are given to show the effectiveness of the results.     

线性不确定随机系统时滞相关的H∞滤波

研究了一类带有时变状态时滞和参数不确定性的连续时间线性随机系统的鲁棒H_∞滤波问题。目的是设计一个线性滤波器使滤波误差动态系统是指数均方稳定的,并满足给定的H_∞性能指标。应用描述符系统模型转换,建立了新的Lyapunov-Krasovskii 函数。通过引入自由加权矩阵,消除了Lyapunov矩阵和系统矩阵的乘积项,从而无需在滤波器设计过程中对Lyapunov矩阵作任何约束,这在很大程度上降低了滤波器设计的保守性。基于LMI方法,针对精确已知随机系统和带有结构不确定性的随机系统,分别提出了时滞相关的鲁棒H_∞滤波器存在的充分性条件。仿真结果表明所提出的设计方法是有效的。     

基于离散小波分解的水文随机过程平稳性检验方法

检验环境变化影响下水文过程是否保持平稳性是开展水文分析与计算、水文模拟预报等的重要前提,本研究提出了水文随机过程平稳性检验方法,首先利用离散小波变换分离水文序列中的确定成分与随机成分,然后选择合适方程描述随机成分,利用Akaike information criterion和Bayesian information criterion计算最优时间滞后阶数,再采用单位根检验方法判别随机成分是否具有平稳性.人工生成序列和实测水文序列分析结果均显示,周期和趋势对随机成分的平稳性检验有很大影响,随着序列信噪比增大,检验结果的准确性变差.相比常规方法直接对原序列进行分析处理的做法,所提方法可首先准确分离确定成分并克服上述因素的干扰,因此较常规方法更加有效,进而可以得到更为合理的水文序列平稳性检验结果.     

随机波动模型参数估计的新算法及其在上海股市的实证

研究用马尔科夫链蒙特卡罗(MCMC)算法估计随机波动模型的参数问题.基于“前向滤波,后向抽样”方法提出一种新算法,并将新算法同原有算法进行了比较.然后利用新算法对上海股市进行波动性分析,发现中国涨跌停板制度对波动的持续性估计有着重要的影响,忽视这些因素将会导致波动的持续性被高估.     

Passivity analysis for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

The problem of passivity analysis is investigated for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, new delay dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the less conservatism of the proposed conditions.     

基于广义随机Petri网的再制造供应链建模与性能分析

为分析再制造供应链的性能,采用了基于广义随机Petri网的建模分析方法,并根据广义随机Petri网与马尔可夫链的同构关系,将广义Petri网模型转化为等价的马尔可夫链模型.通过马尔可夫链及相关数学方法得出再制造供应链的主要性能指标.该方法不仅可以分析整个再制造供应链的性能,还能对各个环节的运作效率做定量分析,为再制造供应链回收再制造模式的选择提供了一个思路.     

THE TRANSITION PROBABILITY MATRIX OF A MARKOV CHAIN MODEL IN AN ATM NETWORK

In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.     

考虑多参考点的基于前景随机占优准则的随机多属性决策

针对随机多属性决策问题,考虑决策者心理行为,提出一种基于多参考点的前景随机占优多属性决策方法.首先,以决策者属性期望作为参考点,根据累积前景理论将决策矩阵转化为损益矩阵.其次,依据前景随机占优准则构建前景随机占优关系矩阵,进而得到前景随机占优度矩阵.进一步,考虑属性相关关系,运用模糊测度得到方案综合占优度矩阵,并运用PROMETHEE Ⅱ方法对方案进行排序.最后,案例分析验证了该方法的可行性和有效性.     

跳变时滞随机系统的鲁棒保性能控制

研究了马尔可夫跳变参数时滞随机系统的鲁棒保性能控制问题。通过构造一个Lyapunov函数,并应用Ito微分公式沿系统对其求微分,再利用线性矩阵不等式(LMI)的性质和广义Ito公式,给出了此类系统保性能控制律存在的充分条件,估计了其保性能值,同时,控制器的设计归结为一族LMI的求解问题。最后,数值算例说明了方法的有效性。     

随机线性二次最优控制在投资组合中的应用

提出一类随机线性二次最优控制问题,给出了一个新的随机黎卡提方程,若此方程有解,就可以得到系统的最优反馈控制;作为其应用,讨论了连续时间的均值-方差投资组合选择问题,其目标是投资组合的最终收益最大,风险最小,通过"嵌入"方法将其转化为随机线性二次最优控制问题,并在非自融资的条件下,得出最优证券组合;最后将其理论应用于实例分析.     

离散时间随机系统的稳定性分析

对由定常非线性随机差分模型所定义状态空间为一般可测空间的离散时间随机系统，本文应用一般状态马氏链遍历性有关理论分析了系统的稳定性问题，给出了由系统相应确定性部分的Ｌｙａｐｕｎｏｖ函数来判别系统稳定的若干充分条件。