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A differential difference type adaptive law and an adaptive iterative learning controller are constructed to ensure the asymptotic convergence of tracking errors in the sense of square error norm on the finite interval, by introducing a Lyapunov-like function, a sufficient condition of the convergence of the method is given.

通过引入微分－差分自适应学习律，设计了一种自适应控制策略，使得跟踪误差在一个有限区间上的积分渐近收敛于零；通过构造Lyapunov-like函数，给出了闭环系统收敛的一个充分条件。

We introduce the general sigma point selection framework, and give two kinds of efficient methods: a reducing the computing complexity by decreasing the number of the sigma point; b scaling the sigma points to influence the effects of the higher order moments, then improve the accuracy of the UT; c Convergence analysis of the UKF, when used as an observer for nonlinear deterministic discrete-time system, is presented. Based on the UKF that captures the posterior mean and covariance accurately to the second or third order term (in terms of Taylor series expansion) for any form of nonlinearity, sufficient conditions to ensure local asymptotic convergence are established.

论文介绍了sigma点的一般选取规则，并给出了两种有效的方法：a通过减少sigma点集合的元素的数目来减少计算复杂度，b通过增加参数来逼近泰勒展开的高阶项，从而提高UT变换的精度；c论文研究了UKF算法应用于非线性确定性离散时间系统时的收敛性问题。

In chapter three, the new concepts of the bifurcation point and asymptotic bifurcation point of compact continuous operators in Menger PN-spaces are introduced. Some sufficient conditions for the existence of the bifurcation point and asymptotic bifurcation point are obtained. And the problems on the intrinsic value and intrinsic element of compact continuous operators are studied in Menger PN-spaces. A series of theorems on the existence of the intrinsic value and intrinsic element are obtained.

第三章，在概率赋范线性空间中提出非线性算子的歧点和渐近歧点的新概念，获得了非线性算子存在歧点和渐近歧点的充分条件；讨论了Menger概率赋范线性空间中非线性算子的固有值和固有元问题，得到了非线性算子存在固有值和固有元的一系列充分条件。

Some sufficient conditions for asymptotic stability of the network's equilibria are presented.

研究网络的渐近稳定性是研究联想记忆及其它应用的关键。

At the same time,the other necessary and sufficient condition is obtained for causality and asymptotic stability of the systems.

目前对于稳定性研究主要采用的是Lyapunov方法，Lyapunov方法在控制系统的研究中起着非常重要的作用，很多的研究学者已将这种方法推广到广义系统中。

Furthermore, a sufficient condition that guarantees the asymptotic stability of the original system was derived.

提出并证明了原系统渐近稳定的充分条件。

It gives a new sufficient condition ensuring global asymptotic stability for cellular neural networks with delay.

给出了时延细胞神经网络全局稳定性的一个新的充分条件。

Sufficient and necessary condition is given for asymptotic stability and exponential stability of one dimension and multi-dimension.

分别给出一维情形和高维情形系统的渐近稳定和指数稳定的充分必要条件。

A sufficient condition is proposed for robust asymptotic stability of the autonomic system in terms of linear matrix inequality.

基于线性矩阵不等式的方法推导了该系统鲁棒渐近稳定的充分条件，并给出了系统状态反馈镇定器和理想滑动模态存在的充分条件。

By constructing suitable Lyapunov functions, we establish sufficient criteria for asymptotic stability of the zero solutions.

利用构造Lyapunov函数的方法，给出了零解的渐近稳定的充分条件。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。