Introduction to Linear Dynamical Systems

 

Textbook and optional references

There is no textbook. Everything we’ll use is posted on the 263 website in pdf format. This year the course reader, which is nothing but a collection of all the material on this website, won’t be available at the bookstore. If you want hardcopy, you can print the course reader yourself, or you can have it printed and bound at, for example, Fedex-Kinko’s in Tresidder, at cost of around $20.

Several texts can serve as auxiliary or reference texts:

• Linear Algebra and its Applications, or the newer book Introduction to Linear Algebra, G. Strang.
• Introduction to Dynamic Systems, Luenberger, Wiley.

You really won’t need these books; we list them just in case you want to consult some other references.

Prerequisites

Exposure to linear algebra and matrices (as in Math. 103). You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transform, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, or dynamics is not required, but can increase your appreciation.

Description

Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, state transfer, and least-norm inputs. Observability and least-squares state estimation.

Lecture Slides

Professor Stephen Boyd, Stanford University, Autumn Quarter 2008-09

1. Overview
2. Linear functions
3. Linear algebra review
4. Orthonormal sets of vectors and QR factorization
5. Least-squares
6. Least-squares applications
7. Regularized least-squares and Gauss-Newton method
8. Least-norm solutions of underdetermined equations
9. Autonomous linear dynamical systems
10. Solution via Laplace transform and matrix exponential
11. Eigenvectors and diagonalization
12. Jordan canonical form
13. Linear dynamical systems with inputs and outputs
14. Example: Aircraft dynamics
15. Symmetric matrices, quadratic forms, matrix norm, and SVD
16. SVD applications
17. Example: Quantum mechanics
18. Controllability and state transfer
19. Observability and state estimation
20. Summary and final comments

All lectures, in 2up format, in one pdf file

Lecture Videos

Professor Stephen Boyd, Stanford University, Autumn Quarter 2008-09

This is a complete list of videos from last year (Autumn Quarter 2007-08)..

Lecture	Slides
Sep 25 ’07	1-1 to 1-24	Flash	iTunes
Sep 27 ’07	2-1 to 2-22	Flash	iTunes
Oct 2 ’07	2-23 to 3-8	Flash	iTunes
Oct 4 ’07	3-9 to 4-4	Flash	iTunes
Oct 9 ’07	4-2 to 5-2	Flash	iTunes
Oct 11 ’07	5-2 to 6-4	Flash	iTunes
Oct 16 ’07	6-4 to 7-2	Flash	iTunes
Oct 18 ’07	7-2 to 8-2	Flash	iTunes
Oct 23 ’07	8-2 to 9-9	Flash	iTunes
Oct 25 ’07	9-9 to 9-26	Flash	iTunes
Oct 30 ’07	10-1 to 10-20	Flash	iTunes
Nov 1 ’07	11-1 to 11-18	Flash	iTunes
Nov 6 ’07	11-18 to 12-9	Flash	iTunes
Nov 8 ’07	12-9 to 13-16	Flash	iTunes
Nov 13 ’07	13-17 to 15-9	Flash	iTunes
Nov 15 ’07	15-10 to 15-24	Flash	iTunes
Nov 27 ’07	15-25 to 16-15	Flash	iTunes
Nov 29 ’07	16-15 to 18-6	Flash	iTunes
Dec 4 ’07	18-6 to 18-30	Flash	iTunes
Dec 6 ’07	18-30 to 20-6	Flash	iTunes

Support Notes

Professor Stephen Boyd, Stanford University, Autumn Quarter 2008-09

Additional background notes.

• Basic notation
• Matrix primer notes (slides 1 | slides 2 | slides 3 | quizzes)
  (All of this material should be very familiar to you.)
• Crimes against matrices
• Least squares and least norm solutions using Matlab
• Solving general linear equations using Matlab
• Low rank approximation and extremal gain problems