EE263: Introduction to Linear Dynamical Systems

Stephen Boyd, Stanford University.


This page is an archive of the course as it was taught by Professor Stephen Boyd in 2008. The materials here should be very close to those used for the video lectures.

Video lectures


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.

Catalog 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. EE263 covers some of the same topics, but is complementary to, CME200.

Course reader

The EE263 course reader is one pdf file consisting of a cover page together with the lecture slides, support notes and homework exercises below.

Lecture slides

  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

Support notes

Additional background notes.

Homework problems

All EE263 homework problems in one file.