ECE1647F Introduction to Nonlinear Systems (Last updated June 30, 2025)

GB342

Instructor

broucke at control.utoronto.ca

Lecture Section	Day and Time	Location	Start Date
LEC 01	Mon 12-2 pm	TBA	September 8

Course notes will be distributed to registered students. In addition the following references are excellent.

Nonlinear Control Systems, 3rd ed. H. Khalil, 2002.
Applied Nonlinear Control, J.-J. Slotine and W. Li, 1990.
Differential Equations, Dynamical Systems, and Linear Algebra. M. Hirsch and S. Smale, 1974.

Here is a timetable of lecture topics. The last column shows activities for the week. This schedule may be updated as the semester progresses.

Lecture	Date	Topics	Due Dates
1	Sept 8	Introduction: nonlinear ODEs; nonlinear phenomena; phase portraits
2	Sept 15	Mathematical background
3	Sept 22	Existence and uniqueness of solutions	Homework 1
4	Sept 29	Comparison lemma, Continuity w.r.t. ic's; finite escape time; limit sets	Quiz 1
5	Oct 6	Invariant sets; Nagumo theorem, stability definitions
6	Oct 13	Thanksgiving
7	Oct 20	Lyapunov stability theory	Homework 2
	Oct 27	Fall Break
8	Nov 4	Barbashin-Krasovksii theorem; converse theorems, exponential stability	Quiz 2
9	Nov 11	LaSalle Invariance Principle; Barbalat's Lemma	Homework 3
10	Nov 18	Stability of perturbed systems	Project Proposal
11	Nov 25	Advanced topics	Quiz 3
12	Dec 2	Advanced topics
13	Dec 15	Final Project

Homework will be submitted on Quercus by 5pm on the due date.