一、线性方程组的消元解法 二、齐次线性方程组有非零解的条件及解的结构 三、非齐次线性方程组有解的条件及解的结构

一、建立测量误差的基本概念 二、观测值的中误差 三、观测值函数的中误差——误差传播定律 四、加权平均值及其中误差

一、几何空间中向量的内积 1. 空间向量及两向量的夹角 (回顾) 实际问题中, 既有大小又有方向的物理量称为向量

本章主要讨论经下五个问题： 1. 向量的概念及其线性运算； 2. 空间直角坐标系与向量的表示； 3. 向量空间的概念； 4. 向量的线性关系及向量组的秩与极大无关组； 5. 向量空间的维数、基及向量的坐标

3.1 Introduction 3.2 Typical test signals for time response of control systems 3.3 First –Order Systems 3.4 Performance of a Second-Order System 3.5 Concept of Stability 3.6 The Relative Stability of Feedback Control Systems

1 Introduction 2 Deterministic Dynamic Programming and Viscosity Solutions 2.1 Introduction 2.2 Value Functions are Viscosity Solutions 2.3 Comparison and Uniqueness 3 Stochastic Control 3.1 Some Probability Theory 3.2 Controlled State Space Models 3.3 Filtering 3.4 Dynamic Programming - Case I : Complete State Information 3.5 Dynamic Programming - Case II : Partial State Information 3.6 Two Continuous Time Problems 4 Robust Control 4.1 Introduction and Background 4.2 The Standard Problem of H∞ Control 4.3 The Solution for Linear Systems 4.4 Risk-Sensitive Stochastic Control and Robustness 5 Optimal Feedback Control of Quantum Systems 5.1 Preliminaries 5.2 The Feedback Control Problem 5.3 Conditional Dynamics 5.4 Optimal Control 5.5 Appendix: Formulas for the Two-State System with Feedback Example 6 Optimal Risk-Sensitive Feedback Control of Quantum Systems 6.1 System Model

Frequency response is the analysis of the response of systemswhen subjected to a sinusoidal change in input. When a linear system is subjected to a sinusoidal input, its ultimate response is also a sustained sinusoidal wave, with the same frequency. The figure below compares the output response of a system (solid line) with a sinusoidal input (dashed line) disturbing the system

System compensation is the process of designing a controller that will produce an acceptable transient response while maintaining a desired steady-state accuracy .These two design objectives are conflicting in most systems ,since small errors imply high gains reduce system stability and may even drive the system unstable .Compensation may be thought of as the process of increasing the stability of a system without reducing its accuracy below minimum acceptable standards

例1.1设R是实数域。考虑最简单而又最基 本的线性函数 y=f(x)=ax, 其定义域和值域都是实数域R,即对R中每一 个实数x,线性函数f使其对应一个函数值ax, 并且具有如下性质:

1.在R中引进内积运算,建立n维欧氏空间概念; 2.讨论欧氏空间的正交基的概念及求法; 3.讨论三维欧氏空间R3中向量积,直线及平面方程等内容 4.建立一般内积空间的概念