ECE1647F Introduction to Nonlinear Systems (Last updated October 6, 2023)

GB434A

Instructor

broucke at control.utoronto.ca

Lecture Section	Day and Time	Location	Start Date
LEC 01	Mon 12:30-2:30pm	BA4164	September 11

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 11	Introduction: nonlinear ODEs; vector fields; nonlinear phenomena
2	Sept 18	Mathematical background
3	Sept 25	Existence and uniqueness of solutions	Homework 1
4	Oct 2	Continuity w.r.t. ic's; finite escape time; Comparison lemma	Quiz 1
5	Oct 9	Thanksgiving
6	Oct 16	Invariant sets; Nagumo theorem
7	Oct 23	Limit sets; Poincare-Bendixson theorem	Homework 2
8	Oct 30	Stability definitions; Lyapunov stability theory	Quiz 2
	Nov 6	Fall Break
9	Nov 13	Barbashin-Krasovksii theorem; exponential stability	Homework 3
10	Nov 20	LaSalle Invariance Principle; Barbalat's Lemma	Project Proposal
11	Nov 27	Converse theorems; boundedness
12	Dec 4	Stability of perturbed systems	Homework 4
13	Dec 18		Final Project

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