UCSB “Contraction Theory for Dynamical Systems”
ME 225FB, Spring 2024
Instructor: Francesco Bullo

This is the website for the UCSB course ME 225FB “Contraction Theory for Dynamical Systems”, Spring 2024. This website's URL is http://motion.me.ucsb.edu/ME225FB-Spring2024.

Course Description

The course provides a mathematical introduction to contraction theory for dynamical systems. Contractivity is a robust and computationally-friendly stability theory. Special emphasis is given to continuous-time differential equations arising in the study of network multi-agent systems, neural networks, gradient dynamical systems, monotone dynamics, and semi-contracting systems. The course is intended primarily for graduate students interested in nonlinear dynamical systems, control, computation and optimization.


Competency in linear algebra, nonlinear dynamical systems, and linear control systems.

Lecture Time and Place

Tue and Thu 12:30-1:45 in GIRV 2110

Course credit

Units: 3. Letter grade.


The course will follow the text: https://fbullo.github.io/ctds
and the slides: https://fbullo.github.io/talks/2023-09-FBullo-ContractionTheory-Tutorial.pdf


Professor Francesco Bullo
Department of Mechanical Engineering
Email: bullo-at-ucsb.edu
Website: https://fbullo.github.io

Office hours = Discussion times

Place: Professor Bullo's Zoom room (see your email)
Time: Tuesdays 4pm-6pm

Please be sure to turn on your video camera when you come to my zoom room, as I will have mine on. I encourage you to use a background.

If you have any questions about the course, please send me email. I will try to respond as quickly as possible. Additionally, I will share questions that are particularly good (and their answers) with the rest of the class by broadcasting my answer to the entire class.

If you come to office hours with questions about homework, please be prepared to show attempts at solving the problem prepared before coming.


Class grade will be determined by:

  • 40% weekly homework assignments

  • 30% final report

  • 30% final presentation

In exceptional cases, I reserve the right to give extra points for excellent performance on the final report and presentation. Please, do not count on it as a way to avoid doing homework assignments.

Homework Self-Grading Scheme

  • Homework is due one week after the corresponding chapter is fully covered in class; precise deadlines will be announced in class.

  • Please write one exercise per page and write clearly for partial credit.

  • To turn in the homework, please scan solutions in a single PDF file and email me the file by the deadline.

  • After the homework deadline, I will email you the solutions (after which no late homework will be accepted).

  • I will ask you to please self-grade your homework and email to me both: (1) the marked homework in PDF form, and (2) the grade. Please self-grade within a week of receiving the solutions.

  • Each exercise in each homework assignment is worth 10 points, unless otherwise marked.

Final Report and Final Presentations

Instructions on the report and presentation will be discussed in class.

Here are some instructions.