# EE263: Introduction to Linear Dynamical Systems

Alex Lemon, Stanford University, Summer Quarter 2014 – 2015

Lectures given by Professor Stephen Boyd are available on YouTube.

1. note: unfortunately, there was a problem scanning the handwritten notes for this lecture, and many slides were lost; also unfortunately, the SCPD office discards the slides after they have been scanned, so we cannot recover the missing slides

1. Example: aircraft dynamics

2. Example: quantum mechanics

3. Controllability and state transfer

4. Observability and state estimation

5. Summary and final comments

## Additional references

Links to the specific YouTube videos covering each lecture are given below, along with references to the textbooks Optimization Models by Calafiore and El Ghaoui and Introduction to Dynamic Systems by Luenberger.

1. Overview

2. Linear Functions

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 2.1, 2.4, 3.1, and 3.2

3. Linear-algebra review

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 2.2, 3.1, 3.2, and 7.2

4. Orthonormal sets and the QR factorization

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 2.2, 2.3, and 7.3

5. Least-squares

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 6.3 and 6.4

6. Least-squares applications

1. YouTube lecture

2. Calafiore and El Ghaoui, section 6.1

7. Regularized least-squares and the Gauss/Newton method

1. YouTube lecture

2. Calafiore and El Ghaoui, section 6.7

8. Least-norm solutions of underdetermined equations

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 6.3, 6.4, and 6.7

9. Autonomous linear dynamical systems

1. YouTube lecture

2. Luenberger, sections 4.1, 4.2, 4.3, 4.4, and 4.6

10. Solution via Laplace transform and matrix exponential

1. YouTube lecture

2. Luenberger, sections 4.6, 5.9, 5.10, 8.4, and 8.5

11. Eigenvectors and diagonalization

1. YouTube lecture

2. Calafiore and El Ghaoui, section 3.3

3. Luenberger, sections 5.2, 5.3, 5.4, and 5.11

12. Jordan canonical form

1. YouTube lecture

2. Luenberger, section 3.9

13. Linear dynamical systems with inputs and outputs

1. YouTube lecture

2. Luenberger, sections 4.5 and 4.7

14. Example: aircraft dynamics

15. Symmetric matrices, quadratic forms, matrix norm, and the SVD

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 4.1, 4.2, 4.3, and 4.4

16. SVD applications

1. YouTube lecture

2. Calafiore and El Ghaoui, sections 5.1, 5.2, and 5.3

17. Example: quantum mechanics

18. Controllability and state transfer

1. YouTube lecture

2. Luenberger, section 8.6

19. Observability and state estimation

1. YouTube lecture

2. Luenberger, section 8.7

20. Summary and final comments