ECE 528 (Analysis of Nonlinear Systems) - Spring 2021

Quick links and important information


  • The Gradescope entry code is: P5XDRG


Course lecture: Tuesdays and Thursdays at 11:00am–12:20pm CT in 1013 ECE Building.

Synchronous Zoom lecture: You may attend the lecture synchronously at

Zoom office hours: The Zoom office hours can be found at

Note: Zoom meetings will require you to authenticate with your Illinois Zoom accounts. Additionally, both of these meetings have passwords which will be sent via Mass Mail, so check your email. If you have not received this password, send me an email from your email address requesting the password and I will provide it. Emails from non-Illinois email addresses will not receive a response.

Media Space channel: Recorded lectures are available at

Course folks

  • Instructor: Roy Dong

    • email: roydong at illinois dot edu

    • office hours: Thursdays, 4pm-5pm CT. (via Zoom)

  • TA: Guilherme Scabin Vicinansa

    • email: gs16 at illinois dot edu

    • office hours: Mondays, 5pm-6pm CT. (via Zoom)

Course description

This is a fundamental first-year graduate course in nonlinear systems. It covers properties of solutions of nonlinear dynamical systems, Lyapunov stability analysis techniques, effects of perturbations, and basic nonlinear control design tools. Proofs of most of the results are presented in a rigorous mathematical style. Familiarity with real analysis (on the level of Math 444 or 447) is important. Math 414 may also be useful for practice in writing rigorous proofs.

The department's course profile for ECE 528 can be found here:

Course logistics


There are 3 ways to view the lectures:

  • In-person lectures

  • Synchronous Zoom lectures

  • Asynchronous lecture recordings

Lectures will be held in-person Tuesdays and Thursdays at 11:00am to 12:20pm CT in 1013 ECE Building.

These lectures will simultaneously be held online via Zoom. I will update the website with the details of the Zoom meeting closer to the start of the semester. You can expect to see it on the “Quick links” section at the top of this page.

IMPORTANT NOTE: You will be required to authenticate with your Illinois Zoom account to attend lectures!

Additionally, recordings of the lecture will be made available afterward. If so desired, you are welcome to take this course asynchronously by watching the lecture recordings. (In other words: lecture attendance is not required. You may use your own judgment as to which method best fits your learning style and current constraints.)

All of this is subject to change.

Here are potential changes that we should be prepared for:

  • The in-person sessions may cease at any time, due to state-level or university-level mandates, or for other extenuating circumstances. Should this happen, synchronous Zoom lectures will continue at the same scheduled time.

  • The synchronous online lectures may switch platforms (e.g. not be held on Zoom). This may happen if there are technical issues in the synchronous format. This will be done in consultation with the course's students.

  • The asynchronous lecture recordings may be hosted on a different platform. Tentatively, I plan on posting these lectures on Media Space, but that may be subject to change as well. I will try to consult with the course's students to weigh the pros and cons before doing so, however.

In summary, please be vigilant in reading course announcements!

Course announcements

Course announcements will be made through the Piazza. Students are responsible for the content in course announcements. So, if I send an announcement that the online lectures are changing a platform, you are held responsible for knowing this information. This is crucial for a hybrid in-person/online format, as I need a way to communicate course logistics and changes to you.

Please adjust your Piazza settings accordingly. More concretely, the expectation is that students are aware of the content of announcements within 24 hours of the announcement's posting. Additionally, you may be responsible for announcements on a shorter time window during lecture time and the take-home midterms and exams, should I announce logistical issues regarding the current lecture (e.g. Zoom is down) or exam Piazza/corrections/hints.


The grade of the course will be determined by: homeworks, a midterm exam, and a final exam.

The final grade calculation will be based on the following weights.

homeworks 50%
midterm exam 20%
final exam 30%


Homeworks will be collected online through the course's Gradescope. HWs will be announced via a course announcement on Piazza, and the due date and time will be given in the announcement. Tentatively, you can expect 5-6 homeworks this semester.

Students are heavily encouraged to typeset their homeworks. Homeworks that are not legible will not be graded, with legibility defined based on our discretion.

Excluding HW0, all homeworks are out of 100 points, and the lowest possible grade is 0 points.

Late policy for homeworks:

  • If a homework is late by (0,24] hours, your homework grade will have 10 points subtracted.

  • If a homework is late by (24,48] hours, your homework grade will have 25 points subtracted.

  • If a homework is late by (48,72] hours, your homework grade will have 50 points subtracted.

  • Homeworks more than 72 hours late will not be accepted. Equivalently, your homework grade will have 100 points subtracted.

Additionally, your lowest homework grade will be dropped. The grade considered is the one after the late policy has been applied, so this is the policy that maximally benefits your grade. HW0 (which simply requires you to set up Gradescope) will not be eligible for dropping.


Both the midterm and final exams will be take-home. You will be able to work on it over a 72-hour period. No late exams will be accepted. The extended time window for the exam is meant to allow you to flexibly allocate time for the exam in your schedule and account for any extenuating circumstances. These exams will be open-book, open-note, and generally open-Internet. However, you may not discuss the exam with any of your colleagues. Exams will also be collected via Gradescope.

Additionally, at the end of the semester, if your final exam grade is higher than your midterm exam grade, then your final exam grade will replace your midterm exam grade.

More details about the logistics of take-home exams will be provided in a course announcement closer to the exam time.

Expectations on collaboration

You are encouraged to discuss the course material with your colleagues. You are welcome to discuss homework problems with your colleagues and work on it collaboratively. The goal of homeworks is to help deepen your understanding of the course material. However, during the 72 hour exam periods for both the midterm and the final exam, you are expected to not discuss the course with any of your colleagues.

For emphasis:

  • For homework assignments, discussion and collaboration is encouraged.

  • For take-home exam time windows, any course discussion is not allowed.

Textbooks and materials

The course will primarily follow:

  • H. K. Khalil, Nonlinear Systems, 3rd edition. Prentice Hall, 2002.

The interested student is also referred to the following textbooks:

  • E. D. Sontag, Mathematical Control Theory, 2nd edition. Springer, 1998.

  • S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, 1st edition. Springer, 1999.

For those wishing to brush up on their analysis for the proofs in this course, I recommend:

  • C. C. Pugh, Real Mathematical Analysis, 2nd edition. Springer, 2015.

Some of these books are made available digitally through the UIUC Library, or made available online by the authors.

Course expectations

I expect all students to contribute to a supportive learning environment and a cooperative community. We are all here to learn, and, I'd like to emphasize this: help each other learn. Students are expected to be civil and respectful.

Throughout the course, you may freely ask questions at any time. There are no stupid questions, and everyone should feel comfortable asking anything during the class. However, I may request that discussions related to such questions be shifted to either office hours or Piazza if there is not enough in-class time to fully resolve any questions.

Academic integrity

All students are subject to the university's academic integrity policies. A quick reference guide, as well as links to the official student code, can be found at: