EXPONENTIAL STABILITY OF LINEAR TIME－VARYING IMPULSIVE DIFFERENTIAL SYSTEMS WITHDELAYS

ＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＴＹＯＦＬＩＮＥＡＲＴＩＭＥ－ＶＡＲＹＩＮＧＩＭＰＵＬＳＩＶＥＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＤＥＬＡＹＳ￥ＧｕａｎＺｈｉｈｏｎｇ（关治洪）；ＬｉｕＹｏｎｇｑｉｎｇ（刘永清）（ＳｏｕｔｈＣｈｉｎａＵｎ...     

测度型区间脉冲系统的稳定性

首次提出并研究了测度型区间脉冲系统的稳定性问题。基于代数Ｒｉｃｃａｔｉ方程，对测度型区间脉冲系统建立了若干全局指数稳定性判据。     

具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性

研究了一类具有时变区间参数的不确定随机线性系统的均方鲁棒稳定性.利用时变区间矩阵的分解技术、矩阵的Kronecker积的性质和Lyapunov函数法,得到了该系统均方鲁棒稳定的几个充分性条件.通过一个数值例子说明了所得的这些充分性条件的有效性和实用性.     

ROBUST ABSOLUTE STABILITY OF GENERAL LURIE SYSTEMS WITH MULTIPLE NONLINEARITIES

1IntroductionandLemmaOneofthemostbasicissuesthatarisesinthecontroltheoryisthero-bustnessofmultivariab1esystems,i.e.theirabilitytomaintainstabilityandperformanceiRthefaceofuncertainties.Inthislight,stabilityisaprimaryconcernedsinceanunstablesystemisobviouslyuseless.Therobustnessofmultivariab1econtrolsystemshasbeenextensivelystudiedinthepast[l,2].Inpaper[2],usingthefrequencyaswellasthetimedomainapproach,thepro-blemofrobustnessofabsolutestabilityofLuriesystemswithnonlinearitiessubjecttomodelvar…     

GLOBAL EXPONENTIAL STABILITY TO A CLASS OF DIFFERENTIAL SYSTEM WITH DELAY

The global exponential stability of the zero solution to a class of differential system with delay is considered.By constructing a suitable type of Lyapunov functional and using some analytical techniques,we derive some criteria to check exponential stability of this system.The results establish a relation between the delay time and the parameters of the system.Two examples are also given to illustrate the validity of the results.     

EXPONENTIAL STABILITY FOR A CLASS OF SWITCHED STOCHASTIC SYSTEMS

In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently "small".     

ON CRITERIA FOR GLOBAL STABILITY OF N-DIMENSIONAL LOTKA-VOLTERRA SYSTEMS

This paper gives the conditions for the existence of a globally stable equi-librium of rz-dimensional Lotka-Volterra systems in the following cases: Lotka-Volterra chain systems and Lotka-Volterra modei between one and multispecies. The conditions obtained in this paper are much weaker than those in [6] and more easily verifiable in application. So the results can be applied to more general Lotka-Volterra models. At the same time, the existence and stability conditions of positive equilibrium points of the above systems are given.     

GLOBAL ROBUST STABILITY OF INTERVAL HOPFIELD NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

In this paper,we implement topological degree theory and Lyapunov-functional methods to obtain the existence and uniqueness of the equilibrium point and its global robust stability for interval Hopfield neural networks with continuously distributed delays.Moreover,the methods used in judging the robust stability are proven practical and easily verifiable.     

变时滞Hopfield神经网络的全局指数稳定性

本文研究了一类具有变时滞Hopfield神经网络的稳定性问题.利用时滞微分不等式方法,获得了几个关于该网络的全局指数稳定性与时滞无关的充分条件,并且给出了此类网络的收敛指数的估计,推广了已知文献的结果.最后给出数值例子证明结论的有效性.     

STABILITY OF LINEAR MEASURE LARGE SCALE SYSTEMS WITH IMPULSIVE EFFECT

ＳＴＡＢＩＬＩＴＹＯＦＬＩＮＥＡＲＭＥＡＳＵＲＥＬＡＲＧＥＳＣＡＬＥＳＹＳＴＥＭＳＷＩＴＨＩＭＰＵＬＳＩＶＥＥＦＦＥＣＴＧｕａｎＺｈｉｈｏｎｇ（关治洪）（ＪｉａｎｇｈａｎＰｅｔｒｏｌｅｕｍＩｎｓｔｉｔｕｔｅ，江汉石油学院，邮编：４３４１０２）ＷｅｎＸ...     

具有时变时滞的不确定离散广义系统的稳定与镇定

本文主要研究具有时变时滞的不确定离散广义系统的稳定性与镇定.利用线性矩阵不等式方法,给出了具有时变时滞的离散广义系统稳定的充分条件,推广了历算广义系统稳定与镇定的相关结果.     

线性不确定系统的稳定控制鲁棒界和多级稳定鲁棒控制

利用李雅普诺夫稳定性理论研究了线性不确定系统的稳定鲁棒控制问题,得到结果“任何一个稳定控制都是具有一定稳定鲁棒界的稳定控制”.进一步地,根据系统的不确定量的范围,设计了多级稳定鲁棒控制策略.最后给出一个例子说明设计步骤的可行性.     

线性不确定系统的鲁棒D型迭代学习控制

研究一类线性不确定系统的鲁棒D型迭代学习控制问题.首先针对一类线性标称控制对象,建立其迭代学习控制的二维模型;然后基于获得的二维模型,利用二维系统稳定性理论,获得系统在迭代初态与期望初态一致和不一致两种情形下的D型迭代学习控制律的存在条件和设计方法;进一步,将所得结果推广至控制对象包含不确定性的情形.所得结果以线性矩阵不等式(LMI)的形式给出,可以方便地利用Matlab中的LMI工具箱求解.最后,数值仿真实例验证了本文所提方法的有效性.     

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SOLUTIONS TO THE QUASILINEAR THERMO-DIFFUSION EQUATIONS WITH SECOND SOUND

This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.     

具时滞Kolmogorov系统的强区间稳定性与部分稳定性

通过得用区间动力系统的稳定性理论和构造适当的Ｌｙａｐｕｎｏｖ科学家函,我们讨论了具离散时滞Ｋｏｌｍｏｇｏｒｏｖ生态系统的渐近性,分别获得了该系统强稳定、部分稳定的充分条件。     

不确定二维多项式族的稳定性检验集合

不确定二维多项式族,包括多胞形二维多项式族,区间二维多项式族,钻石形二维多项式族,其鲁棒稳定性可由其棱边多项式的稳定性确定.如果二维多项式族的不确定参数较多,被检验棱边多项式的数目可能出现所谓组合爆炸问题.为解决这一问题,提出一检验集合,该集合根据棱边二维多项式的凸方向来构造,仅对属于该检验集合棱边二维多项式进行稳定性检验,从而大大地减少被检验的棱边二维多项式数目.给出一例来说明这种新方法的可行性.     

n维时滞Prajneshu生态系统的区间生态稳定

对ｎ维时滞Ｐｒａｊｎｅｓｈｕ＾［１］生态系统ｄｘｉ（ｔ）／ｄｔ＝ｘｉ（ｔ）［ｒｉ＋Σ↑ｎ↓ｊ＝１ａｉｊｌｎｘｊ＋Σ↑ｎ↓ｊ＝１ｂｉｊｌｎｘｊ（ｔ－τｊ）ｉ＝１，２，…，ｎ（１）的区间生态稳定性进行了研究，给出了其区间生态稳定的判别准则。     

EXPONENTIAL STABILITY OF FIRST ORDER DYNAMIC EQUATION ON TIME SCALES

This paper is concerned with the stability of a first order dynamic equation on time scales. In particular,using the properties of the generalized exponential function with time scales,different kinds of sufficient conditions for the exponential stability are obtained.     

一阶广义分布参数系统的指数稳定性

利用退化半群的方法讨论了Hilbert空间中一阶广义分布参数系统的指数稳定性,并给出了判断指数稳定性的充要条件.     

ON THE PARTIAL STABILITY OF IMPULSIVE DIFFERENTIAL EQUATIONS

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＬｅｍｍａｓＣｏｎｓｉｄｅｒｔｈｅｆｏｌｏｗｉｎｇｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈｉｍｐｕｌｓｉｖｅｅｆｅｃｔｓ：ｘ′＝ｆ（ｔ，ｘ），ｔ≠τｋ，△ｘ＝Ｉｋ（ｘ），ｔ＝τｋ，ｋ＝１，２，…，（１）ｗｈｅｒ...