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.

강사

심형보 교수 http://cdsl.kr/~hshim


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


2018년부터는 snui로 시작하는 링크가 동작하지 않는 것 같습니다. 새로운 YouTube 링크를 지속적으로 구하여 제공하려 합니다. 우선은 1강~11강까지만 링크를 update하겠습니다.
12강부터의 새 링크는 2018년 12월 초까지 update 하겠습니다.
 

1. System and State

  1. Introduction to the course   14:58

           https://youtu.be/15-typuvSOs

  2. System   09:21

           https://youtu.be/HvIvMQwWxI4

  3. Classification of Systems   12:38

           https://youtu.be/6Oex8QW796Y

  4. State   15:01

           https://youtu.be/R8kPauDzkcA

  5. Linear State Space Systems   09:29

           https://youtu.be/Dt02sjGKxQw

  6. Time Invariance   12:59

           https://youtu.be/Qr8dM7WVRQs

 

2. Vector Spaces

  1. Fields and Vector Spaces   21:28

           https://youtu.be/AkIwfdly8No

  2. Subspaces   21:16

           https://youtu.be/ldyHFJw-FYU

  3. Linear Independence   12:15

           https://youtu.be/UpqfJm3dm7k

  4. Basis   11:41

           https://youtu.be/p7uDP_GSVII

 

3. Linear Transformations and Matrices

  1. Dimensions   20:50

           https://youtu.be/UaEsMTHDhsY

  2. Change of Basis   09:51

           https://youtu.be/29w7HFes5xM

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

           https://youtu.be/azSExYD5ASI

           * 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

           https://youtu.be/c31v01OhNBo

 

4. Eigenvalues and Eigenvectors

  1. Eigenvalues and Eigenvectors   29:41

           https://youtu.be/bvATQ37IFT4

  2. Independent Eigenvectors and Diagonalization   21:21

           https://youtu.be/M2d22IpwivM

  3. Eigenspace and Generalized Eigenspace   23:06

           https://youtu.be/qzaHykumi-s

 

5. Eigenvectors and Diagonalization

  1. Generalized Eigenvector and Jordan Block   17:40

           https://youtu.be/ajHWIHfyacg

  2. Chain of Generalized Eigenvector   28:09

           https://youtu.be/4laERkXbq7M

  3. Summary and Examples   09:31

           https://youtu.be/TRism15UMao

 

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

  1. Cayley-Hamilton Theorem   14:03

           https://youtu.be/TKHkaMTPHSI

  2. Polynomial Functions of a Square Matrix   22:00

           https://youtu.be/41AADSqOb0c

  3. Minimal Polynomial   09:52

           https://youtu.be/LQBTCrCFSNs

  4. Functions of a Square Matrix   20:09

           https://youtu.be/_8JNJE6w_8g

 

7. Inner Product Spaces, Normed Spaces

  1. Inner Product Spaces   11:49

           https://youtu.be/x1YE2cjhVbE

  2. Normed Spaces   12:55

           https://youtu.be/b04E5y5fhkE

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

           https://youtu.be/BuaJVQsaW_o

  4. Orthonormalization   22:33

           https://youtu.be/R7-1EON75HU

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

           https://youtu.be/gLEbVOOuw1o

 

8. Induced Norm, Quadratic Form, and Related Properties

  1. Induced Norm and Properties   17:17

           https://youtu.be/TmBErGGKxM4

  2. Property of Linear Operator   10:27

           https://youtu.be/mOh7afN2fqY

  3. Adjoint of a Linear Transformation   33:51

           https://youtu.be/Li1fd7Da1NE

  4. Quadratic Forms   16:07

           https://youtu.be/xnEtXRz6sGI

  5. Induced Two Norm of Matrix   17:43

           https://youtu.be/7p_k99pG4z4

           * 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

           https://youtu.be/_s7VLkRE-hU

  2. Existence and Uniqueness of the Solution   33:30

           https://youtu.be/_XzppcvG3aY

  3. State Transition Matrix   10:23

           https://youtu.be/UsG32EUUQwk

  

10. Basics of Linear Time-Invariant System

  1. Matrix Exponential   17:16

           https://youtu.be/lwrswAW5zf8

  2. Properties of State Transition Matrix   04:52

           https://youtu.be/71m-HRp32X8

  3. Variation of Constant Formula   24:07

           https://youtu.be/IaYBV9uCLf8

 

11. Stability of Linear Systems

  1. Equilibrium and Linearization of Nonlinear Model   17:42

           https://youtu.be/q9bXGvZW4LE

  2. Definition of Lyapunov Stability   23:25

           https://youtu.be/M54o-ACimSY

  3. Determination of Stability   17:51

           https://youtu.be/q49deFJjlAo

  4. BIBO Stability of Linear Systems   16:47

           https://youtu.be/D_v1l1drzt8

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

           https://youtu.be/LqIWmbbIUco

 

 


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
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