ECE 780-T09: Network Systems and Control (Spring 2018)

Syllabus Description

Many large-scale natural and engineering systems can be modelled as collections of independent agents or subsystems which interact with one another through physical coupling, communication, or both. Examples include flocking birds, schooling fish, electric power systems, mobile robot teams, and sensor networks. The dynamic behaviour of these network systems depends on the nature of the agents, the nature of the inter-agent physical or communication-based coupling, and most interestingly on the global pattern of interaction between all agents.

This course is concerned with analyzing and designing the dynamics of multi-agent network systems, and is intended primarily for graduate students in engineering and applied math interested in dynamics over networks, cooperative and distributed control, and distributed algorithms. Topics include:

  • theory of nonnegative matrices (Perron–Frobenius theory);

  • graph theory, with an emphasis on algebraic graph theory;

  • discrete-time and continuous-time distributed averaging (consensus) algorithms;

  • positive and compartmental linear systems;

  • circuit theory: graph models, dynamic stability, effective resistance, model reduction;

  • distributed optimization using multi-agent systems;

  • applications to networks of coupled oscillators, viral spread models, sensor networks, power system dynamics, resource allocation problems, and population dynamics.

A complete syllabus is here.


Competency in linear algebra and graduate-level LTI systems theory (ECE 682 or equivalent) is strongly recommended. Exposure to nonlinear dynamical systems theory (ECE 688 or equivalent) is recommended  —  particularly Lyapunov stability theory  —  but is not required.

Lecture Location and Times

Monday, 2:30–5:20pm, EIT 3141


F. Bullo. Lectures on Network Systems (available here and on Amazon)


There will be four substantial assignments. Students may work together on assignments, but the submitted work must be your own. Assignments will be graded for completeness, clarity of thought, and clarity of presentation. Printed solutions will be distributed in class.

  • Assignment 1 (pdf). Due in class on June 4th, 2018.

  • Assignment 2 (pdf). Due in class on June 18th, 2018.

  • Assignment 3 (pdf). Due in class on July 9th, 2018.

  • Assignment 4 (pdf). There will not be an Assignment 4 this year.

  • Note: Some assignment questions will ask you to provide formal mathematical proofs for given statements. A useful introduction to mathematical logic and proof techniques can be found here.


  • Project Handout (pdf).

  • Proposal due via e-mail by June 18th, 2018 (at the latest).

  • Please e-mail me to schedule a 10–15 minute mid-project check-in meeting, for the week of July 9th, 2018.

  • Report due July 25th, 2018 in class.

  • Presentations will be held on July 25th, 2018 in the courses final lecture slot.


There is no midterm or final exam for ECE 780 T09.