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EE263: Introduction to Linear Dynamical Systems

Sanjay Lall, Stanford University, Fall Quarter 2023

Lecture slides

These slides are updated as the course progresses, so we don't recommend downloading them all at the beginning of the quarter.

  1. Overview

  2. Linear functions

  3. Engineering examples

  4. Interpretations of linear equations

  5. Linear algebra review

  6. Range and null space

  7. Rank

  8. Orthogonality

  9. QR factorization

  10. Least-squares

  11. Example: Least-squares navigation

  12. Multi-objective least-squares

  13. Least-norm solutions of underdetermined equations

  14. Recursive estimation

  15. Least-squares fitting

  16. LS via QR factorization

  17. Gauss-Newton method

  18. Eigenvectors and diagonalization

  19. Symmetric matrices

  20. Ellipsoids

  21. Matrix norm

  22. SVD and applications

  23. Autonomous linear dynamical systems

  24. Solution via matrix exponential

  25. Dynamic interpretation of eigenvectors

  26. Jordan canonical form

  27. Linear dynamical systems with inputs and outputs

  28. Controllability and state transfer

  29. Observability and state estimation

  30. Summary and final comments

Optional additional lecture slides

  1. Example: Input design

  2. Example: Estimation/filtering

  3. Example: Least-squares filtering revisited

  4. Extremal-trace problems