课程名称 (Course Name) ： Analysis and design of linear systems

课程代码 (Course Code）： IN26007

学分/学时 (Credits/Credit Hours)： 3/48

开课时间 (Course Term )：  Spring

开课学院（School Providing the Course）:  SEIEE

任课教师（Teacher）:  Qilian Bao

课程讨论时数（Course Discussion Hours）:  4

课程实验数（Lab Hours）:   8

课程内容简介(Course Introduction):

This is a fundamental course on the modern theory of linear systems and control. Fundamental concepts of modern control theory are covered, including systems modeling and solutions in state space, stability, controllability, observability, and pole placement. Furthermore, system similarity transformation, stability and realization, and state controller and observer design will be explained. Computer based tools-Matlab for control system design is also introduced.

教学大纲(Course Teaching Outline):

Chapter1 Introduction

In this chapter, the history of control theory, some basic concepts of control system, and the application of control theory are introduced.

Chapter2 Mathematic description of dynamic system

In this chapter, the state variables and state space description are elaborated. Methods of setting up state space models for dynamic systems are described in detail.

Chapter3 Linear algebra

This chapter focuses on fundamental knowledge on linear algebra, including mathematic review of linear algebra, linear transformation, and computation of exponential matrix.

Chapter 4 Space state solutions and realization

This chapter introduces computation solutions to state space models. The realization of a LTI system in different forms is illustrated.

Chapter 5 Stability analysis

Stability of multi-variable systems is analyzed by using lyapunov methods. Several detective approaches are given based on lyapnov theorems.

Chapter 6 Controllability and observability

This chapter discusses controllability and observability of a system. First, the definitions are given. Then detective methods of controllability and observability of LTI systems are described.

Chapter 7 State feedback and state estimator

In this chapter, design method and design procedure of state feedback based controller are introduced. It focuses on pole placement method. Design method and procedure of state observer are another important part of this chapter. Finally, state feedback control based on pole placement and state observer is discussed.

Chapter 8 Optimal control

In this chapter, the fundamental concepts of optimal control are introduced. Design of LQR controller and its application are also described.

课程进度计划(Course Schedule):

chapter	contents	hours
1	An Introduction	2
2	Mathematic description of dynamic system	4
3	Linear algebra	6
4	Space state solutions and realization	6
5	Stability Analysis	4
6	Controllability and Observability	4
	Lab Project1	4
7	State feedback and state estimator	6
8	Fundamentals of optimal control	4
	Lab Project2	4
	Discussion/Seminar	4
		48

课程考核要求(Course Assessment Requirements)：

The final score is made up of three parts:

1)        Attendance, homework, quiz:                                          30%

2)        Lab projects and reports:                                      30%

3)        Final project report and presentation:                               40%

参考文献(Course References)：

1)        Textbook：Linear System Theory and Design, C.-T. Chen, 3rd Ed., Oxford University Press, 1999.

2)        Reference books: Joao P. Hespanha. Linear System Theory, Princeton University Press, 2009

预修课程（Prerequisite Course）

1)        Classic Control Theory

2)        Linear Algebra