EE263: Introduction to Linear Dynamical Systems

Alex Lemon, Stanford University, Summer Quarter 2013 – 2014

Lectures, problem sessions, and office hours

  • Lectures: Tuesdays and Thursdays, 3.15pm to 5.05pm in Thornton 102

  • Problem sessions: Thursdays (starting 6/26), 9am to 9.50am in Gates B03

  • Office hours (starting the week of 6/30):

    • Tuedays, 1pm to 3pm in Packard 107

    • Wednesdays, 6pm to 8pm in Packard 107

Contact

Course description

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

Prerequisites: linear algebra and matrices as in MATH104; differential equations and Laplace transforms as in EE102A You should have seen the following topics: matrices and vectors, (introductory) linear algebra; differential equations, Laplace transforms, transfer functions. Exposure to topics such as control systems, circuits, signals and systems, and dynamics is not required, but may increase your appreciation of the course material.

Course requirements and grading

  • Weekly problem sets: 20%
    Problem sets will usually be posted on Friday by 5pm, and be due the following Friday by 5pm. Homework should be submitted to the cabinet across the hall from Packard 243. You are allowed, and even encouraged, to work on the homework in groups, but you must write up your own solution. SCPD students should email course staff list for instructions about how to submit homework.

  • Midterm exam: 30%
    The midterm is a 24-hour takehome exam, see the midterm exam page for details.

  • Final exam: 50%
    The final is a 24-hour takehome-exam, see the final exam page for details.

All grades are recorded on CourseWork.

References

There are no required or optional textbooks – everything we will use will be posted on the course website. However, several texts can serve as auxiliary or reference texts.

  • Linear Algebra and Its Applications, G. Strang

  • Matrix Analysis and Applied Linear Algebra, C.D. Meyer

  • Introduction to Dynamic Systems, D. Luenberger

  • Computational Science and Engineering, G. Strang

  • Linear Algebra Done Right, S. Axler

You will not need these books, and none of them cover exactly the material that we will be covering: we only list them in case you want to consult some additional references.