EE263: Introduction to Linear Dynamical Systems

Sanjay Lall, Stanford University, Autumn Quarter 2015

Lecture Slides

These slides are from last year. During the quarter we will post updated versions here.

  1. Overview

  2. Example: Input design

  3. Example: Estimation/filtering

  4. Linear functions

  5. Engineering examples

  6. Interpretations of linear equations

  7. Linear algebra review

  8. Rank

  9. Orthogonality

  10. QR factorization

  11. Least-squares

  12. Example: Least-squares navigation

  13. Example: Least-squares filtering revisited

  14. Least-squares fitting

  15. Recursive estimation

  16. Multi-objective least-squares

  17. Least-norm solutions of underdetermined equations

  18. Eigenvectors and diagonalization

  19. Symmetric matrices

  20. Ellipsoids

  21. Matrix norm

  22. SVD and applications

  23. Extremal-trace problems

    1. Total least squares

  24. Autonomous linear dynamical systems

  25. Solution via Laplace transform and matrix exponential

  26. Dynamic interpretation of eigenvectors

  27. Jordan canonical form

  28. Linear dynamical systems with inputs and outputs

  29. Controllability and state transfer

  30. Observability and state estimation

  31. Summary and final comments

Calendar

  1. 9/22 covered 1.1 to 4.4

  2. 9/24 covered 4.4 to 6.9

  3. 9/29 covered 6.10 to 7.22

  4. 10/1 covered 7.23 to 8.6

  5. 10/6 covered 9.1 to 10.6

  6. 10/8 covered 10.7 to 11.10

  7. 10/13 covered 11.11 to 14.11

  8. 10/15 covered 14.12 to 17.5

  9. 10/20 covered 17.6 to 19.2

  10. 10/22 covered 19.3 to 20.7

  11. 10/27 covered 21.1 to 22.9

  12. 10/29 covered 22.10 to 22.30

  13. 11/3 covered 23.1 to 23.16

  14. 11/5 covered 24.1 to 24.23

  15. 11/10 covered 25.1 to 26.5

  16. 11/12 covered 26.6 to 27.6

  17. 11/17 covered 27.7 to 28.23

  18. 11/19 covered 28.24 to 29.13

  19. 12/1 covered 29.14 to 30.9

  20. 12/3 covered 30.10 to 31.5