UCSB “Nonlinear Network Systems”
ME 225FB, Fall 2018
Instructor: Francesco Bullo

This is the website for the UCSB course ME 225FB “Nonlinear Network Systems”, Fall 2018. This website’s URL is http://motion.me.ucsb.edu/ME225-Fall2018. A pdf version of this documentation is available on the course website.

Offical Description

The course is intended primarily for graduate students interested in nonlinear dynamical systems and nonlinear control systems as arising in cooperative control, distributed algorithms, distributed systems, and network science. Topics will include:

  • a brief review of network systems theory (as in ME269) and of Lyapunov and LaSalle stability theory (as in ME236), as applied to network dynamical systems (averaging, compartmental systems),

  • passivity theory

  • network small gain theory

  • theory of competitive/cooperative and monotone systems,

  • contraction theory (applied to network and diffusively coupled systems)

  • example applications from robotics, industrial control systems, traffic systems, mathematical sociology, and power grids.


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

Lecture Time and Place

Engineering Bldg II, room 2243, ME Classroom
TuTh 9:30am - 10:45am

(Francesco will have to travel once or twice during the quarter; arrangements will be discussed in class. We will discuss the possibility to have make-up classes )

Course credit

Units: 3. Letter grade.


The textbook for this material is not in existence yet. Indeed, this area appears to be not amenable to a sistematic approach. The instructor will present a series of papers and attempt to do so in a coherent way. The list of papers to be discussed will be available shortly before the start of the quarter at the instructor website.

A small fraction of the material is available at
Lectures on Network Systems, May 2018, by Francesco Bullo.
The document is available at http://motion.me.ucsb.edu/book-lns
You are welcome to download the textbook in standard format as well as in slide format.


Professor Francesco Bullo
Department of Mechanical Engineering
Email: bullo-at-engineering.ucsb.edu
Website: http://motion.me.ucsb.edu

Office hours

Place: Room 2325, Engineering Bldg II
Time: To be determined

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.

Grading for ME 225FB

The class grade is based on a final written report and a final oral presentation. Students are encouraged to work in pairs, and choose a project that is relevant to their own area of research.

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