As one of the basic curricula of control specialties,“Modern control theory”has important significance for studying other subjects of control theory ,such as Optimal control、System identification, Robust control and Intelligent control, and it is also widely used in so many fields, such as industry, agriculture, shipbuilding and aviation.
This curricula states the elementary principles of modern control theory and discusses its analysis and synthesis techniques based on “state space method”. It consists of six parts, including state space description of linear system, dynamic analysis of linear systems, controllability and observability of linear systems, state-space synthesis of linear system, and Lyapunov stability analysis.
Through the study of this curricula, we hope that students can correctly establish the mathematical model of all kinds of typical systems, especially the state space model, grasp the analysis method of various system models, and apply state feedback, pole assignment and state observer methods for synthesis and design of complex systems. Finally, students have the ability to engage in control system analysis and research.
“现代控制理论”是控制类专业的一门专业基础课程，本门课程对于学习控制理论的许多学科分支，如最优控制、系统辨识、鲁棒控制、智能控制等具有重要的作用，同时,该理论也对广泛应用于工业、农业、船舶、航空航天等诸多领域。
本课程是以状态空间法为基础阐述了现代控制理论的基本原理以及其分析和综合的方法。共分为六个部分，内容包括线性系统的状态空间描述、线性系统的运动分析、线性系统的运动分析、线性系统的能控性和能观测性、线性系统的状态综合以及李雅普诺夫稳定性分析。
通过学习本课程，希望学生能够正确建立各类典型系统的数学模型，特别是状态空间模型，掌握分析各类系统模型的方法，并且能够通过状态反馈、极点配置和状态观测器构造等方法，进行复杂系统的综合与设计，从而培养学生从事控制系统分析和研究的能力。
第一章 绪论
1.1 系统与控制理论概述
1.2 线性系统理论概述
第二章 线性系统的状态空间描述
2.1 基本概念
2.2 状态空间表达式的建立
2.3 线性时不变系统的特征结构
2.4 状态方程的约当规范形
2.5传递函数矩阵
第三章 线性系统的运动分析
3.1 运动分析概述
3.2 状态转移矩阵
3.3 脉冲响应矩阵
第四章 线性系统的能控性和能观测性
4.1 基本概念
4.2 能控性判据
4.3 能观测性判据
4.4能控规范形与能观测规范形实现
4.5 对偶性与结构分解
第五章 系统运动的稳定性
5.1 基本概念
5.2 李氏判据第一法
5.3 李氏判据第二法及线性系统应用
5.4 构造李雅普诺夫函数的规则化方法
第六章 线性反馈系统的时间域综合
6.1 状态反馈与输出反馈
6.2 状态反馈极点配置
6.3 状态反馈镇定
6.4 状态观测器
Chapter 1 Introduction
1.1 An overview of system and modern control theory
1.2 An overview of linear system theory
Chapter 2 State-space description of the linear systems
2.1 Basic concept
2.2 Established methods of state space representation
2.3 Characteristic structure of linear time invariant system
2.4 Jordan Standard form of state equation
2.5 Transfer function matrix
Chapter 3 Dynamic analysis of linear systems
3.1 An overview of dynamic analysis
3.2 State transition matrix
3.3 Impulse response matrix
Chapter 4 Controllability and observability of linear systems
4.1 Basic concept
4.2 Criterion of controllability
4.3 Criterion of observability
4.4 Realization of controllable canonical form and observability canonical form
4.5 Duality and structure decomposition
Chapter 5 Stability of system motion
5.1 Basic concept
5.2 First method of Lyapunov
5.3 Second method of Lyapunov and its application to linear system
5.4 Regularization method to construct Lyapunov function
Chapter 6 Time domain synthesis of linear feedback systems
6.1 State feedback and output feedback
6.2 Pole assignment using state feedback
6.3 System stabilization using state feedback
6.4 State observer