李亚普诺夫方法的发展与历史性成就——纪念李亚普诺夫的博士论文“运动稳定性的一般问题”发表一百周年

本文论述了李亚普诺夫方法的发展,全文共分七部分:1 李亚普诺夫方法产生的历史背景;2 在李亚普诺夫原数学模式中的发展;3 在反馈系统中的发展与应用;4 李亚普诺夫方法与时变、不确定系统;5 在理论上的进一步发展;6 比较原理与李亚普诺夫方法;7 结束语。     

连续时间回归网络的稳定性分析

连续时间回归网络的稳定性分析张兰玲刘贺平孙一康（北京科技大学自动化系北京１０００８３）关键词连续回归神经网络，渐近稳定，绝对稳定．收稿日期１９９６－０９－２６１引言回归网络稳定性的分析大多是采用李亚普诺夫直接法［１］，这种方法的关键在于李亚普诺夫函数...     

含二维临界部分系统的李亚普诺夫函数构造

含二维临界部分系统的李亚普诺夫函数构造苗原（清华大学计算机系北京１０００８４）李春文（清华大学自动化系北京１０００８４）关键词中心流形，稳定性，非线性系统，李亚普诺夫函数．收稿日期１９９５－１０－０６１引言李亚普诺夫函数不仅是重要的判稳工具，还与使系...     

非线性系统零解稳定性判定的广义二次型方法

为了寻找一种能充分利用矩阵理论构造非线性系统李亚普诺夫函数的方法．首先提出分量函数矩阵和广义二次型函数等概念，得到了如果一个函数的导数具有某种特定形式。则不需处理旋度方程．便可直接得到该函数的若干定理；然后提出一种构造李亚普诺夫函数和判定非线性系统零解稳定性的广义二次型方法．并举例说明了该方法的应用．理论和实例表明，该方法是一种充分利用矩阵特性，适用范围广且不需处理旋度方程的方法．     

一类离散时间切换系统鲁棒控制器设计

考虑一类非线性离散时间切换系统的鲁棒二次镇定和渐近镇定问题．利用公共李亚普诺夫函数方法和多李亚普诺夫函数方法，分别设计了切换系统鲁棒状态反馈控制器和输出反馈控制器，保证了切换系统的二次稳定性和渐近稳定性．仿真结果验证了所提出算法的有效性．     

基于条件李亚普诺夫指数的混沌系统的脉冲同步研究

基于条件李亚普诺夫指数,对混沌系统的脉冲同步形式和同步范围进行了研究,突破了传统的基本假设．计算机仿真证明了该方法的有效性和正确性．此外,作为该方法的重要基础,本文给出脉冲同步系统的条件李亚普诺夫指数计算方法．     

基于后推设计的直接自适应模糊控制

针对一类严格反馈不确定非线性动态系统，提出一种直接鲁棒自适应模糊控制新方案．利用模糊系统的逼近能力、后推设计方法和积分型李亚普诺夫函数，依次确定各虚拟控制及模糊系统中可调参数的自适应律，并最终确定出控制律．为改善控制系统的性能，引入逼近误差的自适应补偿项．通过李亚普诺夫方法，证明了闭环系统是一致终结有界的．仿真结果表明了该方法的有效性。     

二维齐次高阶临界系统的稳定性判别算法

本文给出了一种判别二维高次齐次非线性临界系统的稳定性的算法，这一算法对中心流形是２维高次的系统通过构造李亚普诺夫函数来判稳有良好的效果，依据这种算法编制成的程序对随机产生的４０个临界非线性系统，均顺利地找到了相应的李亚普诺夫函数。     

多胞型不确定性随机时滞系统鲁棒H∞控制

考虑凸多胞型不确定性的随机时滞系统的鲁棒H∞控制问题,分别运用参数化和非参数化的李亚普诺夫函数，给出解决问题的充分条件.通过求解一组线性矩阵不等式(LMI),设计所需状态反馈控制器,所得到的闭环系统均方渐近稳定，且满足所需要的H∞性能指标,其中参数化的李亚普诺夫函数具有更小的保守性.通过算例验证了方法的有效性.     

一类多变量非线性动态系统的模糊辨识及鲁棒分析

对一类非线性多变量未知动态系统，提出一种模糊辨识器，设计中采用ＩＦ－ＴＨＥＮ推理规则来构造多变量模糊逻辑系统，实现对系统中未知函数的逼近；应用李亚普诺夫合成方法和奇异摄动理论，研究模糊辨识器的稳定性和鲁棒性。     

Non-conservative ultimate bound estimation in LTI perturbed systems

A closed formula for ultimate bound estimation in LTI systems with non-vanishing perturbations is presented. The formula, based on geometrical properties of the system, provides an alternative to Lyapunov's second method based study. Although it is not proven that the bound obtained is always less conservative than the Lyapunov's bound, some examples are introduced where the estimations are significantly improved. An extension of the idea for nonlinear systems is also sketched.     

李雅普诺夫指数谱的研究与仿真

李雅普诺夫指数在研究动力系统的分岔、混沌运动特征中起着重要的作用。该文介绍了李雅普诺夫指数的定义、计算原理及数值计算的实现方法，应用Matlab软件，编制了计算李雅普诺夫指数的程序，分析了一维、二维和三维非线性动力系统中分岔和混沌与李雅普诺夫指数之间的关系。绘制了逻辑斯蒂映射、埃农映射和洛仑兹方程的分岔图，并计算了相应的李雅普诺夫指数。实例的计算机仿真表明李雅普诺夫指数是研究分岔、混沌运动，解决工程实际问题的有效方法之一。     

Direct method for transient stability studies in power system analysis

This paper deals with recent advances in developing direct methods for studying the transient stability problem of single-machine and multimachine power systems. The paper starts out with the construction of the mathematical model that is usually employed in the analyis of power system transient stability. Computer simulation methods are then briefly discussed, and it is indicated why accurate direct methods for transient stability investigations would be most welcome. It is shown that the classical direct methods, which are based on energy considerations, can be derived and generalized by means of Lyapunov's second method. The main purpose of the paper is to give an exposition of the interesting results that have been obtained by applying Lyapunov's second method to the transient stability problem of single-machine and multimachine power systems. In the final portion of the paper some areas for further research are discussed.     

The Kalman-Yacubovich lemma in adaptive control system design

The design of model-reference control systems by Lyapunov's direct method has been considered by a number of authors. New results presented in this note pertain to the design of these systems with the aid of the Kalman-Yacubovich lemma derived in connection with the Lur'e problem.     

离散滞后广义系统稳定域的定量估计

利用Lyapunov方法讨论离散滞后广义系统, 并给出了该类系统的零解一致稳定区域和渐近稳定区域的大小估计. 当初始扰动是在稳定区域时, 离散滞后广义系统的初始值问题的解一致稳定; 当初始扰动是在渐近稳定区域时, 离散滞后广义系统的初始值问题的解趋于零. 所举的仿真例子描述了该方法的应用.     

非线性系统降价观测器的构造

本文主要基于李雅普诺夫稳定性概念、指数观测器和系统指数可观的概念[1]探讨了如下 式所示系统建立降价观测器的理论及方法.x=Ax+f(x),y=Hx     

Asymptotic Stability of Interval Time-Delay Systems

In this paper we consider the asymptotic stability of linear interval time-delay systems on the base of using Lyapunov's direct method and methods of interval analysis. A sufficient condition of asymptotic stability is obtained using the concept of Lyapunov-Krasovsky functional.     

Stability and estimates for the convergence of solutions for systems involving quadratic terms with constant deviating arguments

In this paper, we shall consider systems of differential equations involving quadratic terms with constant deviating arguments. Stability of the systems is investigated by employing the second Lyapunov's method with a special rational function. This function provides convergence rate estimates as well as offers explicit sufficient conditions for the asymptotic stability of solutions.     

Stability analysis of fuzzy large-scale systems

This paper is concerned with the stability problem of fuzzy large-scale systems. Each of them consists of J interconnected subsystems which are represented by Takagi-Sugeno fuzzy models. A stability criterion in terms of Lyapunov's direct method is proposed to guarantee the asymptotic stability of fuzzy large-scale systems. Finally, an example is given to demonstrate the results.