渐近的

Compared with deterministic systems, the infinitesimal generator for the system is a second-order differential operation. In this dissertation, we designed the quartic control Lyapunov function and systematically design the state-feedback and output feedback adaptive controller using integrator backstepping methodology. The closed-loop system is asymptotically stable in the large.

与确定性系统相比，随机系统的Lyapunov函数的微分运算包含二阶导，所以设计适当形式的控制Lyapunov函数十分关键，本文设计了四次型的控制Lyapunov函数，并应用积分反推技术，给出了状态反馈及输出反馈自适应控制器和鲁棒自适应控制器的设计方法，证明了闭环系统概率意义下的渐近稳定性和有界稳定性。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation. In part I, a group of sufficient conditions is given on continuation of solutions and three groups of sufficient conditions are given on boundedness of solutuicns of equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

For the admissible time-delay as well as non-linear disturbances, an time-delay integral transformation and a matrix inequality method are developed. The design of observer and stability of error systems can be represented as a matrix inequality, matrix of observer gain and condition of global asymptotically stable of error systems are obtained. An example is included to illustrate the pratical applicability of the proposed theory.

对于允许的时滞和非线性干扰，利用一个变换和不等式技巧，将观测器的设计，误差方程的稳定性归结为一个矩阵不等式，给出了观测器增益阵的解析式和误差方程全局渐近稳定的条件，一个例子说明了所提定理的可行性。

Now by using Dai's exact solution formula and studying the asymptotical behavior controlcondition and using the series expression of the famous Riemann Zeta-function in number theory,after introducing and proving a new representation theory of inverse Laplace transformation wedirectly obtained Chen's solution formulae and their unique existence condition without usingLaplace transformation and〓 inverse formula.

本文从带消发散参数的严格解出发，通过研究渐近行为控制条件，利用数论中著名的Riemann-Zeta函数的级数表示，引入并证明一个逆Laplace变换的新的表示定理，直接导出了陈等发展的级数解，并得到了级数解的存在、唯一性条件。

According to the result, the confidence region of unknown parameters in single-index models is constructed. Finally, we consider the test of correlation and heterogeneity for hierarchical nonlinear mixed-effects models. According to Laplace approximation expansion of integrated log-quasilikelihood, a class of score test statistics is proposed. Under some very mild conditions, we prove the asymptotic distribution of the test statistics is a standard X~2-distribution. Through a Monte Carlo simulation study, the finite sample performance is examined.

最后，我们研究的第四个问题是分层非线性随机混合效应模型的相关性与异方差性检验问题，依据对数拟积分似然的Laplace近似展开提出了检验统计量，在一些正则条件下，得到了检验统计量的渐近分布是一个标准的χ~2-(来源：d7d7A65BC论文网www.abclunwen.com)分布，通过Monte Carlo模拟研究了其小样本的表现，实例验证了其实际应用。

Firstly, Receding horizon H〓 control based on state feedback with terminal constraints is proposed for systems with disturbance inputs and parameter perturbations. Linear Fractional Transformation and some existed results on Receding horizon H〓 control for systems without perturbations are introduced.

首先针对同时存在外界输入扰动和自身参数摄动的不确定线性时变系统，利用线性分式变换和现有的一些无摄动系统滚动时域H〓控制的结果，得到了基于状态反馈的终端约束滚动时域H〓控制器的设计方法，并给出了控制律存在和使闭环系统渐近稳定的充分条件。

Under the conditions that the system without impulse effect satisfies the one-side Lipschitz condition, and the impulsive terms satisfy the corresponding Lipschitz conditions, a sufficient condition which can be easily checked the stability of the analytic solution is obtained.

在不受脉冲影响的原方程满足单边Lipschitz条件，及脉冲项满足相应的Lipschitz条件的情况下，给出了一个容易判别的解析解渐近稳定的充分条件。

Using integral equation theory and"contraction mapping"theorem, we prove that this model has a unique solution.

接着用压缩映象原理证明了此模型解的存在唯一性，这为讨论经济系统的稳定性奠定了数学基础，又通过对定常的投资方程渐近稳定性的研究和非定常投资方程Liapunov稳定性研究，我们分别讨论了积累率、劳动力和科技进步对经济增长的作用，进而指出只有依靠科技进步才能实现经济的持续增长，才能真正提高人民的生活水平。

Also, it is deduced from the conclusions of maximum likelihood estimator that the performance of estimators is independent on source number if the number of snapshots used in estimator is large enough.

证明了它们在低信噪比情况下仍具有渐近无偏的估计性能；另外，利用最大似然估计器的相关结论，证明了在快拍数足够大的情况下，估计器的估计性能与信源数目的多少无关。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。