Linear System Theory Course Teaching Outline

I.The Basic Information of the Course

Course Number:202012420026

The EnglishName of theCourse：Linear System Theory

The ChineseName of theCourse：线性系统理论

In-classHours andAllocation(total class hours:32, classroom teaching: 20classhours, classroom discussion:12classhours.)

Credit(s):2

Semester:1

AppliedDiscipline(ProfessionalDegreeCategory)：Mathematics

CourseObjectOriented：AcademicMaster and AcademicDoctor

EvaluationMode:ProcessEvaluation

TeachingMethod:HeuristicTeaching,Seminar-styleTeaching

CourseOpening Department:College of Mathematical Sciences

II.Prerequisite Course

Mathematical analysis, Linear algebra, complex function, ordinal differential equation

III. The Objectives and Requirements of the Course

The course is animportantcoursefor Mathematics and applied mathematics,and is thefoundationfor the students to understand the method of analysis and control of linear system theory. The main contents of thiscourseinclude state space analysis,analysis and synthesisof linear system, and Robustness analysis. The aim of the course is to cultivatescientific thinking and abstract thinkingof the studentson the system theory, such that the students cangrasp the basic ideas, theories and methodsof lineat system, andhave the ability to solvepracticalproblems, and also lay a solid theoretical foundation for learning other disciplines in the field of system and control theory.

IV. The Content of the Course

Chapter 1 Mathematical description of linear system (6 classhours)

1.1 Transfer function description of linear system

1.2 State space description of linear system

1.3 Comparison and conversion between twodescriptions

1.4 Algebraic equivalence oflinear system

Course for Ideological and Political Education:

Prof.Zhaozhi Guan, mathematician, expert in systems and control,Academician of CAS, The pioneer and disseminator of modern control theory in China, the first director of Institute of system science, Chinese Academy of Sciences. Prof. Guan graduated from Mathematics Department of YenchingUniversity in 1941, went to France for studying in 1947, Learn fromFrechet, who isa great mathematician, founder of general topology and functional analysis. When the founding of new China in 1949, Prof. Guan stop studying and return to the motherland. After returning to China, Prof. Guan assisted Guo Moruo with other comrades in the preparatory work for the establishment of the Chinese Academy of Sciences. In 1952, he participated in the preparation for the establishment of Institute of mathematics, Chinese Academy of Sciences. In 1979, he participated in the establishment of Institute of system science, Chinese Academy of Sciences. Prof. Guan devoted to the research and development of mathematics, control science and system science. Since the 1960s, He devoted himself to the research, popularization and application of modern control theory for the development of military and aerospace industries. He has made a series of important contributions in satellite orbit measurement, missile guidance, submarine control and other projects.

Chapter 2Kinematic analysisof linear system (6 classhours)

2.1 The meaning of motion analysis

2.2 State transition matrix and its properties

2.3 Motion analysis of linear time-varying system

2.4 Motion analysis of linear time-invaryingsystem

Chapter3Controllability and observability(8 classhours)

3.1Definitions of controllability and observability

3.2Controllability criterionof linear time-varying system

3.3Controllability criterionof linear time-invarying system

3.4 Duality principle and observabilitycriterion

3.5Controllabilityindex and observabilityindex

3.6 Canonical form ofControllabilityand observability

Chapter4Motion stabilityof linear system (6 classhours)

4.1Lyapunovstability

4.2 Stability determinationof linear time-varying system

4.3Stability determinationof linear time-varying system

Chapter5Pole assignment and eigen-structure assignment(6 classhours)

5.1Controlof linear system

5.2Pole assignment and existence of Solutions

5.3 State feedback pole assignment eigen-structure assignment

5.4 Output feedback feedback pole assignment eigen-structure assignment

Course for Ideological and Political Education:

Prof. Siying Zhang, graduated from the department of machinery of Wuhan University in 1948; started as a teacher in Northeast Institute of technology in 1949, and was a professor, the director of Engineering Mechanics Department, the director of Automation Research Institute. He joined the Communist Party of China in 1950. From 1957 to 1959, he studied automatic control theory in the Department of mathematics and mechanics, Moscow State University, the former Soviet Union. In 1986, he founded the journal of control and decision and acted as the editor in chief. He was elected as a academician of the Chinese Academy of Sciences in 1997. He has been engaged in the theoretical research of motion stability, optimal control and differential game for a long time. He was one of the pioneers of education and scientific research in the field of control science and system science in China, and he was a winner of National "May 1st" labor medal. He was engaged in the research of motion stability and optimal control in the early stage, including the new type of finite time interval stability. He psarticipated in the development of anti-tank missile, solved the key problems of control system, and achieved outstanding results. In the study of differential games, the extremum property of qualitative differential games was put forward and demonstrated, and the principle of qualitative maximum was given, which makes the two kinds of problems of quantitative and qualitative unified on the basis of extremum principle, forming a new system, and giving a series of applications. In the research of master-slave game, some new concepts such as penalty amount and quantitative calculation were put forward. A new research direction of symmetry and similarity structure of complex control system was put forward. He studied the nonlinear system and composite large-scale system extensively, and the rules of the system were obtained, and such kind of structure can reduce the dimension, decompose, simplify the system, and got the simplified control rules.

V. Reference Books, Reference Literatures, and Reference Materials

1.段广仁.线性系统理论(第三版).科学出版社,2016。

2.仝茂达.线性系统理论和设计.中国科学技术大学出版社, 2012。

3.李先允.现代控制理论基础.机械工业出版社,2007。

4. Gene F. Franklin, J. David Powell, Abbas Emami-Naeini. Feedback Control of Dynamic Systems. 6th ed. Beijing : Publishing House of Electronics Industry, 2013.

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