非线性非自治系统零解的稳定性及部分稳定性研究

讨论了非线性非自治系统未被扰动运动的全变元及关于部分变元的稳定性、一致稳定性及全局稳定性，给出了几个判定准则，这些定理允许Lyapunov函数的导数为变号函数，改进了已有文献中的有关结果。     

关于扰动微分方程组零解部分变元的稳定性

本文讨论未被扰动运动关于部分变元的稳定性，一致稳定性和全局渐近稳定性，给出了一种判定，改进了文［１］中的相应定理。     

离散大系统关于部分变元的关联集合稳定性

本文利用Liapunov函数方法，研究了离散大系统关于部分变元的关联集合稳定性，给出了关于部分变元关联集合稳定性的几个基本定理的一些充分条件.     

两类稳定性定理的改进

本文对两类稳定性定理进行了改进.通过K函数性质,将原来马尔金稳定性定理中V函数导数在有限时间内可变号的性质,推广到长时间内,得到了新的非自治微分方程解的稳定性判定方法.对积分收敛判定定理中的不足进行了补充说明,并且对定理进行了改进和推广,得到了新的一致稳定性判定方法.     

Volterra积分微分方程关于部分变元的稳定性

本文给出了 Volterra 积分微分方程的零解关于部分变元的稳定性定义,并建立了几个判定定理。     

变系数退化时滞微分系统解的稳定性

利用拉什密辛型定理讨论了变系数退化时滞微分系统解的稳定性，并给出了一个具体的判定定理．     

大系统关于部分变元的指数稳定性

本文利用Lyapunov函数法讨论了大系统关于部分变元的指数稳定性,得到了一些定理.通过把高阶系统看作低阶关联子系统的复合,从而使独立子系统的部分变元指数稳定性反映了整个系统同样的特性.     

关于稳定性的几个基本定理

本文给出了非自治常微分方程稳定性，一致稳定性，渐近稳定性与一致渐近稳定性的几个定理。这些定理允许Lyapunov函数的导数为变号函数，放宽了Marachkov定理对系统状态变量变化率有界的要求，推广了文[4-7]的相应结果。     

广义Eady模型的非线性稳定性

对于广义Eady模型，分别讨论了密度函数是常数函数与指数函数两种情形，利用变分原理，考虑到动量守恒的约束条件，得到了优化的Poincare不等式，从而得到了新的非线性稳定性定理，并且得到了在径向长度分别不大于纬向长度的0．84402倍及0．86068倍时（这对于地球的实际情况是成立的），非线性稳定性判据与线性稳定性判据是一致的．     

离散系统稳定性定理的推广与部分稳定的李亚普诺夫函数

本文给出具有常号差分的李亚普诺夫函数的离散系统稳定性定理和不稳定性定理;并给出常系数线性离散系统特征值满足λ_iλ_j≠1与不满足λ_iλ_j≠1时部分变元稳定情况下李亚普诺夫函数的构造方法.     

一类非线性动力系统实用稳定域的研究及应用

借助于李雅普诺夫函数讨论了一类非线性动力系统的实用稳定性和实用稳定域的估计问题,得到了实用稳定域存在的充分条件,给出了一类动力系统实用稳定域的具体形式.通过具体实例说明了所给条件的实用性,改进了已有的结果.     

Semiglobal practical integral input-to-state stability for a family of parameterized discrete-time interconnected systems with application to sampled-data control systems

Semiglobal practical integral input-to-state stability (SP-iISS) for a feedback interconnection of two discrete-time subsystems is given. We construct a Lyapunov function from the sum of nonlinearly-weighted Lyapunov functions of individual subsystems. In particular, we consider two main cases. The former gives SP-iISS for the interconnected system when both subsystems are semiglobally practically integral input-to-state stable. The latter investigates SP-iISS for the overall system when one of subsystems is allowed to be semiglobally practically input-to-state stable. Moreover, SP-iISS for discrete-time cascades and a feedback interconnection including a semiglobally practically integral input-to-state stable subsystem and a static subsystem are given. As an application of the results, these can be exploited in controller design for a sampled-data system in the framework proposed in Nešić et al. (1999) and Nešić and Angeli (2002). We illustrate such a controller design via an example.     

On the practical global uniform asymptotic stability of stochastic differential equations

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations (SDEs) by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and the global practical uniform exponential stability of solutions of SDEs based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result.     

PRACTICAL STABILITY OF DYNAMIC SYSTEMS WITH IMPULISIVE SOLUTIONS

ＰＲＡＣＴＩＣＡＬＳＴＡＢＩＬＩＴＹＯＦＤＹＮＡＭＩＣＳＹＳＴＥＭＳＷＩＴＨＩＭＰＵＬＩＳＩＶＥＳＯＬＵＴＩＯＮＳＨｅＪｉａｎｘｕｎ（贺建勋）（ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，厦门大学，邮编：３６１００５）Ａｂｓｔｒａｃｔ：Ｐｒａｃｔｉｃａｌｓｔａ...     

电力市场实用稳定性的判定条件

首次把实用稳定性的理论用于电力市场稳定性的研究中.结合Alvarado提出的电力市场动态模型,利用微分代数方程与特征值技术,从理论上研究电力市场的实用稳定性,并且给出了判断电力市场实用稳定、一致实用稳定和实用渐近稳定性的充分条件.利用这些实用稳定性条件,对于Alvarado给出的数值算例,可方便地利用初始数据判断电力市场模型的实用稳定性,并通过实例提供了假设模型中某个参数在电力市场变化中起主要作用,如何控制电力市场模型实用稳定性的方法.最后利用Maple软件包给出了参数变化引起模型实用稳定和不稳定的图形演示.     

Stability and boundedness criteria of nonlinear impulsive systems employing perturbing Lyapunov functions

This paper develops a new comparison principle for nonlinear impulsive differential systems, then the stability, practical stability and boundedness of impulsive differential systems are proved by using the method of perturbing Lyapunov functions. The notion of perturbing Lyapunov functions enables us to discuss stability properties of impulsive systems under much weaker assumptions. The reported novel results complement the existing results. It may provide a greater prospect for solving problems which exhibit impulsive effects.     

Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations

This paper studies the practical stability of the solutions of nonlinear impulsive functional differential equations. The obtained results are based on the method of vector Lyapunov functions and on differential inequalities for piecewise continuous functions. Examples are given to illustrate our results.     

Practical Stability in the pth Mean of Stochastic Differential Equations with Discontinuous Coefficients

In this paper,we give sufficient conditions to analyze the practical stability in the pth mean of stochastic differential equations with discontinuous coefficients.The Lyapunov-like function plays an important role in analysis.Some numerical computations are carried out to illustrate the theoretical results.     

时间尺度上脉冲动力系统的实用稳定性

对时间尺度上脉冲动力系统进行研究,利用Lyapunov类函数和比较原理,得到这类系统实用稳定性的充分条件.     

线性时滞系统实用稳定性的一个简明判据

利用比较的方法，获得了线性时滞系统实用稳定性的一个简单判定定理．