### 선형대수와 선형시스템 기초

소개
• 선형 대수의 내용과 선형 동적 시스템의 내용을 포함한 수업입니다. 영문명은 Linear Algebra and Linear Dynamical Systems 입니다.
• 2013년 2학기에 서울대학교 전기공학부 학부 4학년을 대상으로 진행한 내용을 서울대학교 교수학습센터의 도움으로 동영상으로 제작하였습니다.
• 이찬화, 오상록 조교 및 교수학습센터 박준이, 박정은 선생님의 지원을 받았고, 전문 촬영팀의 도움으로 동영상의 화질이 양호합니다.
• 현재 아래와 같은 방법으로 무료 수강이 가능합니다. 과목명이 '최신제어기법'이라고 표기되어 있습니다.

### 교재

Jin Heon Seo, Lecture Note, 2013
단, 동영상 청취에 따로 교재가 필요하지 않습니다.  다만 화면 아래의 PDF 문서를 참고로 다운 받을 수 있습니다.

### 강의 동영상

1. System and State

1. Introduction to the course   14:58

2. System   09:21

3. Classification of Systems   12:38

4. State   15:01

5. Linear State Space Systems   09:29

6. Time Invariance   12:59

2. Vector Spaces

1. Fields and Vector Spaces   21:28

2. Subspaces   21:16

3. Linear Independence   12:15

4. Basis   11:41

3. Linear Transformations and Matrices

1. Dimensions   20:50

2. Change of Basis   09:51

3. Linear Transformations, Null Spaces, and Range Spaces   23:10

* 18:18부터 나오는 Dimension Theorem의 증명 중 R(L) = span(S)에 관한 증명은 불완전하며, 교재 Theorem 2.14의 증명을 참고하기 바랍니다.

4. Matrix Representations of Linear Transformations   15:39

4. Eigenvalues and Eigenvectors

1. Eigenvalues and Eigenvectors   29:41

2. Independent Eigenvectors and Diagonalization   21:21

3. Eigenspace and Generalized Eigenspace   23:06

5. Eigenvectors and Diagonalization

1. Generalized Eigenvector and Jordan Block   17:40

2. Chain of Generalized Eigenvector   28:09

3. Summary and Examples   09:31

6. Cayley-Hamilton Theorem, Functions of a Square Matrix

1. Cayley-Hamilton Theorem   14:03

2. Polynomial Functions of a Square Matrix   22:00

3. Minimal Polynomial   09:52

4. Functions of a Square Matrix   20:09

7. Inner Product Spaces, Normed Spaces

1. Inner Product Spaces   11:49

2. Normed Spaces   12:55

3. Relationship between Inner Product Space and Normed Space   10:40

4. Orthonormalization   22:33

5. Norm of Linear Transformations and Induced Norms   14:30

8. Induced Norm, Quadratic Form, and Related Properties

1. Induced Norm and Properties   17:17

2. Property of Linear Operator   10:27

3. Adjoint of a Linear Transformation   33:51

5. Induced Two Norm of Matrix   17:43

* 13 20초 부근에서 characteristic equation = \sum_{i=1}^{d} ( lambda - lambda_i )^{ \eta_i }에서 \eta_i m_i의 잘못입니다. (바로 다음에 다른 방법으로 설명하기 때문에 전개상 큰 문제는 없습니다.)

9. Linear Dynamic System and State Transition Matrix

1. Linear Dynamic System and Modeling   13:09

2. Existence and Uniqueness of the Solution   33:30

3. State Transition Matrix   10:23

10. Basics of Linear Time-Invariant System

1. Matrix Exponential   17:16

2. Properties of State Transition Matrix   04:52

3. Variation of Constant Formula   24:07

11. Stability of Linear Systems

1. Equilibrium and Linearization of Nonlinear Model   17:42

2. Definition of Lyapunov Stability   23:25

3. Determination of Stability   17:51

4. BIBO Stability of Linear Systems   16:47

5. BIBO Stability and Poles of LTI Systems   09:36

12. Lyapunov Theorem, Stable and Unstable Subspaces

1. Lyapunov Theorem   43:36

2. Stable and Unstable Subspaces   16:36

13. Controllability

1. Definition of Controllability   09:02

2. Controllability Gramian   21:59

3. Property of Controllability Gramian   13:08

4. Controllability of Linear Systems   28:33

14. Observability and Duality

1. Definition of Observability   14:43

2. Observability Gramian   15:32

3. Observability of Linear Systems   11:35

4. Observability of Linear Time-Invariant Systems   16:37

5. Duality   10:20

15. Controllable and Observable Canonical Forms

1. Controllable Canonical Forms   34:26

2. Example for Controllable Canonical Forms   12:29

3. Observable Canonical Forms   16:42

16. Structure of Uncontrollable Systems

1. Controllable Subspace   11:45

2. Properties of Controllable Subspace   10:57

3. Controllability Decomposition   35:11

4. Stabilizability   09:55

17. Structure of Unobservable Systems

1. Unobservable Subspace   17:49

2. Observability Decomposition   19:51

3. Detectability   12:25

4. Kalman Decomposition   13:24

18. Popov-Belevitch-Hautus Test

1. PBH Test for Observability   21:53

2. PBH Test for Detectability   13:18

3. PBH Test for Controllability and Stabilizability   15:15

4. Consideration of Complex Numbers and Examples   22:05

19. State Feedback and Observers

1. State Feedbacks   33:17

2. State Observer   24:45

20. Reduced-order Observer, Separation Principle

1. Review on State Feedback and Observer   06:59

2. Reduced-order Observer   23:38

3. Full-order Observer Based Controller Design and Separation Principle   21:43

4. Reduced-order Observer Based Controller Design and Separation Principle   14:40

21. Realization

1. Minimal Realization   30:20

2. Controllable and Observable Canonical Form Realization   10:30

3. MIMO Case of Canonical Form Realization   20:55

22. Regulation and Tracking

1. Set-point Regulation   31:33

2. Robust Tracking and Disturbance Rejection   29:03

3. Optimal Control   15:49

Ċ
Hyungbo Shim,
Mar 24, 2014, 9:45 PM