前言 第1章 线性系统的数学描述 1.1 系统的输入-输出描述 1.1.1 基本概念 1.1.2 线性松弛系统的脉冲响应 1.1.3 具有因果性线性松弛系统的输入-输出描述 1.1.4 系统的传递函数矩阵 1.2 状态变量描述 1.2.1 状态变量与动态方程 1.2.2 齐次状态方程的解 1.2.3 非齐次状态方程的解 1.2.4 时不变系统的解 1.2.5 动态方程的等价 1.3 传递函数矩阵和矩阵分式描述 1.3.1 传递函数矩阵描述 1.3.2 传递函数矩阵的史密斯-麦克米伦形 1.3.3 矩阵分式描述 1.3.4 传递函数矩阵的零、极点 1.4 微分算子描述 1.4.1 系统矩阵 1.4.2 系统的零、极点 第1章参考文献 第2章 线性系统的可控性和可观测性 2.1 线性系统的可控性 2.1.1 可控性的基本含义和直观例子 2.1.2 可控性的定义 2.1.3 时间函数向量的线性无关性 2.1.4 线性时变系统的可控性判据 2.1.5 线性定常系统的可控性判据 2.1.6 线性定常系统的可控性指数 2.2 线性系统的可观测性 2.2.1 可观测的基本含义和直观例子 2.2.2 可观测性的定义 2.2.3 线性时变系统的可观测性判据 2.2.4 线性定常系统的可观测性判据 2.2.5 线性定常系统的可观测性指数 2.3 线性定常系统可控、可观测的其他判据 2.3.1 Jordan形动态方程的可控性和可观测性 2.3.2 可控、可观测的几何判据 2.4 线性系统的输出可控性和输入可观测性 2.4.1 输出可控性 2.4.2 输出函数可控性 2.4.3 输入函数可观测性 2.5 线性时变系统的一致可控性和一致可观测性 2.5.1 一致可控性 2.5.2 一致可观测性 2.6 线性系统的对偶原理 2.6.1 线性时变系统的对偶原理 2.6.2 线性定常系统的对偶原理 2.7 线性系统的结构分解 2.7.1 线性时变系统在非奇异变换下的可控性和可观测性 2.7.2 线性定常系统的可控性结构分解 2.7.3 线性定常系统的可观测性结构分解 2.7.4 线性定常系统结构的规范分解 第2章参考文献 第3章 线性定常系统的标准形和实现 3.1 单变量系统的标准形 3.1.1 可控标准形 3.1.2 可观测标准形 3.2 多变量系统的标准形 3.2.1 龙伯格第一可控标准形 3.2.2 龙伯格可观测标准形 3.2.3 块三角标准形 3.3 实现的基本概念和性质 3.3.1 基本概念 3.3.2 传递函数矩阵的可实现性 3.3.3 最小实现的特点 3.4 可控性、可观测性的频域形式 3.4.1 传递函数的可控性和可观测性 3.4.2 传递函数矩阵的可控性和可观测性 3.5 传递函数和传递函数矩阵的最小实现 3.5.1 传递函数的最小实现 3.5.2 传递函数矩阵的最小实现 3.5.3 最小实现的汉克尔矩阵法 第3章参考文献 第4章 线性系统的稳定性 4.1 稳定性的基本概念和定理 4.1.1 稳定性的基本概念 4.1.2 李雅普诺夫第二法的主要定理 4.2 线性时变系统的稳定性判据 4.2.1 线性时变系统稳定的特点 4.2.2 线性时变系统稳定性的两个定理 4.2.3 线性时变系统的李雅普诺夫函数 4.3 线性定常系统的稳定性判据 4.3.1 基本定理 4.3.2 线性定常系统的李雅普诺夫函数 4.3.3 李雅普诺夫第二法在系统综合方面的应用 4.4 线性系统的BIBO稳定性和BIBS稳定性 4.4.1 线性时变系统的BIBO稳定性 4.4.2 线性定常系统的BIBO稳定性 4.4.3 线性系统的BIBS稳定性和总体稳定 第4章参考文献 第5章 线性系统时域中的反馈控制与综合 5.1 状态反馈的特征配置 5.1.1 状态反馈系统的可控性与可观测性 5.1.2 单变量系统的极点配置 5.1.3 多变量系统的极点配置 5.1.4 系统的可镇定问题 5.1.5 状态反馈的特征结构配置 5.2 输出反馈的极点配置 5.2.1 输出反馈系统的可控性与可观测性 5.2.2 常值输出反馈配置极点的基本定理 5.2.3 常值输出反馈配置极点的算法 5.3 动态输出反馈补偿器 5.4 解耦控制问题 5.4.1 解耦控制问题的提法 5.4.2 系统状态反馈解耦的充要条件 5.4.3 状态反馈解耦的极点配置 5.4.4 稳态解耦问题 5.4.5 输出反馈解耦问题 5.5 状态观测器和带观测器的动态系统 5.5.1 全维状态观测器 5.5.2 降维状态观测器 5.5.3 函数观测器 5.5.4 带观测器反馈的动态系统 第5章参考文献 CONTENTS Chapter 1 Mathematical Description of Linear Systems 1.1 Input-Output Description of Systems 1.1.1 Basic Concepts 1.1.2 Impulse Response of Linear Relaxed Systems 1.1.3 Input-Output Description of M ultivariable Linear Relaxed Systems with Causality 1.1.4 Transfer Function Matrix of Systems 1.2 State Variable Description 1.2.1 State Variable and Dynamical Equations 1.2.2 Solutions of a Homogeneous State Equation 1.2.3 Solutions of a Non-Homogeneous State Equation 1.2.4 Solutions of Time-Invariant Systems 1.2.5 Equivalence of Dynamical Equations 1.3 The Description of Transfer Function Matrices and Matrix Fractions 1.3.1 The Description of Transfer Function Matrices 1.3.2 Smith-McMillan Form of Transfer Function Matrices 1.3.3 The Matrix Fraction Description 1.3.4 Zero-Poles of a Transfer Function Matrix 1.4 Differential Operator Description 1.4.1 System Matrix 1.4.2 Zero-Poles of Systems Chapter 1 Exercises Chapter 2 Controllability and Observability of Linear Systems 2.1 Controllability of Linear Systems 2.1.1 Basic Connotations and Perceivable Examples of Controllability 2.1.2 The Definition of Controllability 2.1.3 Linear Independence of Time-Function Vectors 2.1.4 Controllability Criterions of Linear Time-Varying Systems 2.1.5 Controllability Criteria of Linear Time-Invariant Systems 2.1.6 Controllability Indices of Linear Time-Invariant Systems 2.2 Observability of Linear Systems 2.2.1 Basic Connotations and Perceivable Examples of Observability 2.2.2 The Definition of Observability 2.2.3 Observability Criterions of Linear Time-Varying Systems 2.2.4 Observability Criterions of Linear Time-invariant Systems 2.2.5 Observability Indices of Linear Time-Invariant Systems 2.3 Other Criteria of Controllability and Observability for Linear Time-Invariant Systems 2.3.1 Controllability and Observability of Dynamic Equations in Jordan Form 2.3.2 Geometric Criterion of Controllability and Observability 2.4 Output Controllability and Input Observability of Linear Systems 2.4.1 Output Controllability 2.4.2 Output Function Controllability 2.4.3 Input Function Observability 2.5 Uniform Controllability and Uniform Observability of Linear Time-Varying Systems 2.5.1 Uniform Controllability 2.5.2 Uniform Observability 2.6 Duality Principle of Linear Systems 2.6.1 Duality Principle of Linear Time-Varying Systems 2.6.2 Duality Principle of Linear Time-Invariant Systems 2.7 Structure Decomposition of Linear Systems 2.7.1 Controllability and Observability of Linear Time-Varying Systems with Non-Singular Transformation 2.7.2 Controllability Structure Decomposition of Linear Time-Invariant Systems 2.7.3 Observability Structure Decomposition of Linear Time-Invariant Systems 2.7.4 Canonical Decomposition of Structure of Linear Time-Invariant Systems Chapter 2 Exercises Chapter 3 Canonical Forms and Realization of Linear Time-Invariant Systems 3.1 Canonical Forms of Single-Variable Systems 3.1.1 Controllable Canonical Form 3.1.2 Observable Canonical Form 3.2 Canonical Forms of Multivariable Systems 3.2.1 Luenberger First Controllable Canonical Form 3.2.2 Luenberger Observable Canonical Form 3.2.3 Block-Triangle Canonical Form 3.3 Basic Concepts and Properties of Realization 3.3.1 Basic Concepts 3.3.2 Realizability of Transfer Function Matrices 3.3.3 Characteristics of Minimal Realizations 3.4 Controllability and Observability in Frequency Domain 3.4.1 The Controllability and Observability of Transfer Functions 3.4.2 Controllability and Observability of Transfer Function Matrices 3.5 Minimal Realization of Transfer Functions and T ransfer Function Matrices 3.5.1 Minimal Realization of Transfer Functions 3.5.2 Minimal Realization of Transfer Function Matrices 3.5.3 The Hankel Matrix Method for Minimal Realization Chapter 3 Exercises Chapter 4 Stability of Linear Systems 4.1 Basic Concepts and Theorems of Stability 4.1.1 Basic Concepts of Stability 4.1.2 Main Theorems of Lyapunov's Second Method 4.2 Stability Criteria for Linear Time-Varying Systems 4.2.1 Characteristics of Stability of Linear Time-Varying Systems 4.2.2 Two Theorems for the Stability of Linear Time-Varying Systems 4.2.3 Lyapunov Function of Linear Time-Varying Systems 4.3 Stability Criteria for Linear Time-Invariant Systems 4.3.1 Basic Theorems 4.3.2 Lyapunov Function of Linear Time-Invariant Systems 4.3.3 Applications of Lyapunov's Second Method in System Synthesis 4.4 BIBO Stability and BIBS Stability of Linear Systems 4.4.1 BIBO Stability of Linear Time-Varying Systems 4.4.2 BIBO Stability of Linear Time-Invariant Systems 4.4.3 BIBS Stability of Linear Systems Chapter 4 Exercises Chapter 5 Feedback Control and Synthesis of Linear Systems in Time Domain 5.1 Eigen Placement with State Feedback 5.1.1 Controllability and Observability of System with State Feedback 5.1.2 Pole Assignment of Single-Variable Systems 5.1.3 Pole Assignment of Multivariable Systems 5.1.4 Stabilization Problem of Systems 5.1.5 Eigenstructure Assignment with State Feedbacks 5.2 Pole Placement with Output Feedback 5.2.1 Controllability and Observability of Systems with Output Feedback 5.2.2 Basic Theorems of Pole Assignment with Constant Output Feedback 5.2.3 Pole Assignment Algorithm with Constant Output Feedback 5.3 Dynamical Output Feedback Compensator 5.4 Decoupling Control Problems 5.4.1 The Statement of Decoupling Control Problem 5.4.2 Necessary and Sufficient Condition for Decoupling Systems with State Feedback 5.4.3 Pole Assignment of Decoupling Systems with State Feedback 5.4.4 Steady State Decoupling Problem 5.4.5 Decoupling Problem with Output Feedback 5.5 State Observer and Dynamic Systems with State Observer 5.5.1 Full-Dimensional State Observers 5.5.2 Reduced-Dimensional State Observers 5.5.3 Function Observers 5.5.4 Dynamical Systems with State Observer Feedback Chapter 5 Exercises
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