上海交通大学电子信息与电气工程学院硕士课程内容介绍《线性系统理论》

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上海交通大学免费考研网/2012-12-28

《线性系统理论》

课程代码	X032504	学分/学时	3.0/54	开课时间	秋
课程名称	线性系统理论
开课学院	电子信息与电气工程学院
任课教师	汪小帆
面向专业	(null)
预修课程	自动控制原理

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课程实验数

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课程内容简介

通过本课程的学习，要求学生达到1.　掌握线性系统理论的基本知识及其分析方法，能够用状态空间表达式来描述系统，并根据系统的微分方程建立其状态空间表达式的方法。2.　掌握系统特征值的求取方法，掌握线性定常系统非齐次方程的解和线性时变系统的解的求取方法，以及离散时间系统状态方程的两种解法。3.　掌握能控性、能观性的定义及各自的判别准则。4.　掌握用李雅普诺夫第一法和第二法分析系统的稳定性的方法。5.　掌握状态反馈和状态观测器设计的基本方法6.　掌握频域理论的基本知识7.　对线性系统理论的新发展有所了解。Through the study of this course, the students are required to:1. Master the fundamental knowledge and the analytic methods of linear system theory, be able to describe the system by state space representation and establish the state space representation according to the differential equation of the system.2. Master the methods to obtain the characteristic roots of the system, the solution to the inhomogeneous equation in linear time-invariant and linear time-variant system, and two methods to solve the state equation in the discrete time system.3. Master the definition of controllability and observability and its respective criteria.4. Master the methods to analyze the stability of a system by Lyapunov first method and Lyapunov second method.5. Master the basic design methods of state feedback and state observer.6. Master the fundamentals of the frequency domain theory.7. Have a general understanding of the new development in the linear system theory.

课程内容简介（英文）

Through the study of this course, the students are required to:1. Master the fundamental knowledge and the analytic methods of linear system theory, be able to describe the system by state space representation and establish the state space representation according to the differential equation of the system.2. Master the methods to obtain the characteristic roots of the system, the solution to the inhomogeneous equation in linear time-invariant and linear time-variant system, and two methods to solve the state equation in the discrete time system.3. Master the definition of controllability and observability and its respective criteria.4. Master the methods to analyze the stability of a system by Lyapunov first method and Lyapunov second method.5. Master the basic design methods of state feedback and state observer.6. Master the fundamentals of the frequency domain theory.7. Have a general understanding of the new development in the linear system theory.

教学大纲

第一章概论 3学时第二章线性系统的状态空间描述 4学时一、系统按状态空间描述的分类二、化输入输出描述为状态空间描述三、状态方程的对角线规范形和约当规范形四、由状态空间描述导出传递函数矩阵五、线性系统在坐标变换下的特性六、组合系统的状态空间描述第三章线性系统的运动分析4学时一.线性定常系统的运动分析二.线性定常系统的状态转移矩阵三.线性定常系统的脉冲响应矩阵四.线性时变系统的运动分析五.线性连续系统的时间离散化六.线性离散系统的运动分析第四章　线性系统的能控制性和能观性8学时一.能控性和能观测性的定义二.线性连续时间系统的能控性判据三.线性连续时间系统的能观测性判据四.对偶原理五.线性离散时间系统的能控性和能观测性六.能控制规范形和能观规范性： SISO七.能控规范形和能观规范性：MIMO八.线性系统的结构分解第五章系统运动的稳定性8学时一.外部稳定性和内部稳定性二.李亚普诺夫意义下运动稳定性的一些基本概念三.李亚普诺夫第二方法的主要定理四.线性系统的状态运动稳定性的判据五.离散时间系统的状态运动稳定性及其判据第六章线性反馈系统的时间域综合10学时一.状态反馈和输出反馈二.极点配置问题：可配置条件和算法三.镇定问题：可镇定条件和算法四.解耦控制问题：可解耦条件和算法五.跟踪问题：无静差性和鲁棒控制六.线性二次型最优控制问题七.引入观测器的状态反馈控制系统的特性第七章多项式矩阵理论 6学时一.多项式矩阵二.奇异和非奇三.单模矩阵四.初等变换五.埃尔米特形六.公因子和最大公因子七.互质性八.列次数和行次数九.既约性第八章传递函数矩阵的分式描述和结构特性8 学时考试 3学时Chap. 1 Introduction 3 contact hoursChap. 2 State space representation of linear systems 4 contact hours1. System classification in state space representation2. Input/output system representation to state space representation3. Diagonal canonical form and Jordan canonical form of state equations4. State space representation to transfer function matrix5. Properties of linear systems under coordinate transformation6. State space representation of combinatorial systemsChap. 3 Dynamic analysis of linear systems 4 contact hours1. Dynamic analysis of linear time-invariant systems2. State transition matrix of linear time-invariant systems3. Impulse response matrix of linear time-invariant systems4. Dynamic analysis of linear time-variant systems5. Temporal discretization of linear continuous systems6. Dynamic analysis of linear discrete systemsChap. 4 Controllability and Observability of Linear Systems 8 contact hours1. Definition of controllability and observability2. Criteria of controllability of linear continuous-time systems3. Criteria of observability of linear continuous-time systems4. Duality theorem5. Controllability and observability of discrete-time systems6. Controllable canonical form and observable canonical form of SISO systems7. Controllable canonical form and observable canonical form of MIMO systems8. Structural decomposition of linear systemsChap. 5 Stability of Dynamic systems 8 contact hours1. Exterior stability and interior stability2. Fundamentals of dynamic stability in the sense of Lyapunov3. Main theorems of Lyapunov second method4. Criteria of state dynamic stability of linear systems5. State dynamic stability and corresponding criteria of discrete-time systemsChap. 6 Linear feedback system in time domain 10 contact hours1. State feedback and output feedback2. Pole assignment problem: assignable conditions and algorithms3. Stabilization problem: conditions and algorithms4. Decoupling control problem: conditions and algorithms5. Tracking problem: zero steady-state error and robust control6. Linear quadratic optimal control problem7. Observer-introduced state feedback control systems

课程进度计划

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课程考核要求

平时作业和测验４０％期末考试６０％（开卷，2.5小时）Homework and quiz: 40%Final Exam: 60% (open book and notes, 2.5 hours)

参考文献

1. Linear System Theory, 2nd Edition, by Dazhong Zheng, published by Tsinghua University Press, 2002.2. Chen C T. Linear System Theory and Design, 2nd ed., 1984, 3rd. ed., 1999. 3. Rugh, W J. Linear System Theory, 2nd ed., Prentice-Hall, 1996