This dissertation studies stability and H_ ∞, control problems for classes of switched nonlinear systems. Lyapunov function method and differential geometry method are two major methods adopted in the study.

A Differential Geometrical Approach for the Solution of KdV Equations

解KdV方程的微分几何方法

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Put forward Riemannian metric-based nearest center neighbor classifier ( RMNCC) on the basis of differential geometry, correlating the feature extraction based on PCA and ICA and classification in radar target recognition on the foundation of mathematics.

针对PCA、ICA特征提取方法，基于微分几何的数学理论，综合考虑了雷达目标距离像识别中的特征提取与分类识别，提出基于黎曼度量的最近中心邻分类器。

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Chaotic Colpitts oscillator systems are studied by using the theories of differential geometry and nonlinear control systems.

利用微分几何和非线性系统控制理论，研究由控制输入驱动的混沌Colpitts振荡器系统的控制问题。

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Proposed method is based on two previously developed approaches: the first one is the differential geometric approach to extract linear features; second one is road contour extraction based on Active Contour Models ( also known as Snake).

提出的方法主要基于以下两条途径：其一，微分几何方法提取线性结构的中心线；其二，基于主动轮廓模型（又被称为Snake）的道路边界提取。

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In this paper, referring to great lot of scientific and technical literatures about worm and CNC, establish mathematical model of cylindrical worm on the basis of the differential geometry and three-dimensional geometry of space-related knowledge.

本文在查阅大量与蜗杆和CNC齿轮测量中心有关的国内外科技文献的基础上，利用微分几何和空间立体几何的相关知识建立了多种常用圆柱蜗杆的理论模型。

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This article has designed the overall hardware system of the induction motor based on the differential geometry decoupling control, given the hardware structure chart. The production of the control signal and the driven enlarged and isolated circuit of PWM for this system are also introduced.

对感应电动机基于微分几何解耦控制的硬件系统进行了整体设计，给出了控制系统硬件结构图，并对硬件控制系统的电压空间矢量PWM控制信号的产生和PWM驱动放大与隔离电路分别进行了介绍；

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This work introduces a kind of design method of nonlinear H ∞ control and discusses its performance of disturbance attenuation.

本文提出了一种基于微分几何反馈线性化理论的非线性H∞控制设计方法，并对这种方法的干扰抑制性能给予了讨论。

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In the area of modern differential geometry and mathematical physics, Clifford algebra is now known to play a more and more important role.

在近代微分几何和数学物理的研究领域中，Clifford代数起着越来越重要的作用。

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Curvature pinching problem plays an important role in global differential geometry.

曲率pinching问题是整体微分几何中很重要的一部分。

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Similar to methods of differential geometry theory, equivalent theorem between differential-algebraic systems' passivation and KYP property was given, the necessary and sufficient passive condition for differential-algebraic systems is given by introducing M derivative.

利用类似微分几何理论的方法，通过引入微分代数系统的M导数，推出了微分代数系统无源与KYP特性等价的定理和微分代数系统无源性的充分必要条件。

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An improved coordinate transform is proposed and then the differential geometry approach can be directly used to obtain the nonlinear control strategy of SSSC.

提出了一种改进的坐标变换，使得微分几何方法可直接应用于求解静止同步串联补偿器（SSSC）非线性控制策略。

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In this paper, velocity harmonization and acceleration harmonization of a2R-1P3R two-arm robot have been studied for special-shaped surface stone with the differential geometry theory and D-H method.

用微分几何理论和D-H法研究了2R-1P3R双臂机器人用于异形石材加工的速度协调和加速度协调，导出了由工艺给定的切削加工速度求解各关节运动速度和加速度的计算公式。

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In this paper, we generalize the Cartan's lemma to ∧ 2 ( v), and obtain.

本文将现代微分几何中著名的Cartan引理，推广到二次外形式空间（？）~2（V~），得出两个定理。

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For varying operation conditions and electric loads over a wide range, combined with PI control law, the method of nonlinear decoupling by using differential geometry approach is introduced into the control design for boiler-turbine systems. The implementation and the robustness of the control method are analyzed.

针对火电机组运行状况和负荷大范围变动的情况，该文将用微分几何法进行非线性解耦和PI调节律结合的思想引入到控制系统的设计中，并且分析了鲁棒性和实用性；

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The differential structure of extended epicycloid bevel gear tooth surface is analyzed when formatted on free-form bevel gear milling machines.

分析了Free form型铣齿机上用成形法加工延伸外摆线锥齿轮时的齿面微分几何结构。

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When H.Hopf studied the homology of compact Lie group, he gave the concept of Hopf algebra.

自H.Hopf研究紧李群同调时提出了Hopf代数概念之后，人们发现它与李代数、微分几何、代数拓扑及统计物理具有广泛的联系。

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Dynamic Analysis of Multi& Constrained Systems Using the Method of Differential Geometry

多个约束系统动力学分析的微分几何方法

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Fractal theory is a new branch of nonlinear scientific research. It studies the smooth and irregular geometric form of nonlinear system.

分形是非线性科学研究中的一个新分支，主要研究对象是非线性系统中的不光滑和不规则的几何体，分形已经被广泛的应用于各个学科领域。

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The thesis expands the drawing scope of geometric constraint solving by increasing cubic Bezier curve as a new geometric primitive.

通过增加三次Bezier曲线作为一个新的几何体，可以扩大几何约束求解算法的作图范围。

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The shape of FDC body was irregular. It covers house, regular geometry or irregular geometry in modeling of environment simulation.

FDC外形不规则；在环境模拟的建模中，涉及到房屋等规则几何体和植物等不规则几何体。

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