EE263: Introduction to Linear Dynamical Systems

Lecture Slides

These slides are from last year's lectures by professor Sanjay Lall, which are based on Professor Stepehn Boyd's original slides. The slides should cover most of the material discussed in class but occasionally we might discuss topics not covered in the slides. The students are encouraged to take notes in such cases.

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