EE263: Introduction to Linear Dynamical Systems

Lecture Slides

These slides are from last year. 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 and Gauss-Newton Method

17. Least-norm solutions of underdetermined equations

18. Autonomous linear dynamical systems

19. Solution via Laplace transform and matrix exponential

20. Eigenvectors and diagonalization

21. Dynamic interpretation of eigenvectors

22. Jordan canonical form

23. Linear dynamical systems with inputs and outputs

24. Symmetric matrices

25. Ellipsoids

26. Matrix norm

27. SVD and applications

28. Extremal-trace problems

29. Controllability and state transfer

30. Observability and state estimation

31. Summary and final comments