ECE 515/ME 540 (Control System Theory and Design) - Fall 2019 - Syllabus

Course description

Feedback control systems emphasizing state space techniques. Basic principles, modeling, analysis, stability, structural properties, optimization, and design to meet specifications.

The department's course profile for ECE 515 can be found here:

For a more detailed list of topics covered, see the bottom of this syllabus.


The class meets on Tuesdays and Thursdays from 2pm to 3:20pm in 3017 ECE Building.

  • Instructor: Roy Dong

    • email: roydong at illinois dot edu

    • office: 142 CSL

    • office hours: 3:30pm to 5pm on Tuesdays in 142 CSL

  • TA: Ivan Abraham

    • email: itabrah2 at illinois dot edu

    • office hours: 3:30pm to 5pm on Mondays in 3020 ECE Building (capacity 30+ students)

    • office hours: 10am to 11am on Thursdays in 3036 ECE Building (capacity 10 students)

Starting Monday, Sept. 23, we will also begin to hold informal homework parties. If you are learning this material for the first time, or struggling with any concepts, please come to 3020 ECE Building on Mondays from 3:30pm to 6:30pm. The TA will be present for the first 1.5 hours; he will leave at 5pm. However, you are encouraged to stay, chat, and work on homework problems together. Please leave the room in a clean state when you exit.

In summary: homework parties from 3:30pm to 6:30pm on Mondays in 3020 ECE Building.


The grades will be broken down as follows.

homeworks 45%
midterm exam 1 15%
midterm exam 2 15%
final exam 25%

You may check your grades at any time on Gradescope (, which we will be using as the gradebook for the class.


Homeworks are generally due on Gradescope on Thursdays at 2pm, prior to the start of lecture. Any variations of this due date will be announced on Piazza as well as written on the homework assignment itself.

No late homeworks will be accepted.

You may drop your lowest homework grade. This dropped homework is meant to account for any personal events or extenuating circumstances that may arise. No exceptions, extensions, or other variations will be given; if something happens that greatly interferes with your ability to complete assignments this semester, grading will be determined by the university's policy on such extenuating circumstances.

Allot yourself time to upload a PDF of your homework to the website. Failure to upload a homework assignment due to technical issues will also be absorbed by the one-dropped-homework policy.

Students are heavily, heavily encouraged to typeset their homeworks. LaTeX proficiency is an absolute requirement for many, many fields of research, and the homeworks for this course are a good place to begin building these skills. It will also make uploading PDFs of your homework to Gradescope much easier.

If you choose to hand-write homeworks instead, you may scan them. I recommend the Adobe Scan app ( to do so. Homeworks are required to be legible. This is a comment on both handwriting and scan quality. The definition of legibility is at our discretion, which is another reason typesetting your homework is recommended.

A quick guide to setting up LaTeX, as well as sample templates for homework will be provided on Piazza.


Midterm exams

There will be two midterm exams throughout the semester. They will be during normal class hours.

  • Midterm 1: Thursday, October 24

  • Midterm 2: Thursday, November 21

During the first midterm, you will be allowed one reference sheet. During the second midterm, you will be allowed two reference sheets.

Reference sheets must be on an 8.5’’-by-11’’ sheet of paper. (This paper size is typically called ‘Letter’ paper.) Both sides may be used, and these reference sheets can be either hand-written or typed.

Final exam

There will be one final exam.

  • Final Exam: Wednesday, December 18, 8am to 11am in 3017 ECEB

During the final exam, you will be allowed three reference sheets.

Reference sheets must be on an 8.5’’-by-11’’ sheet of paper. (This paper size is typically called ‘Letter’ paper.) Both sides may be used, and these reference sheets can be either hand-written or typed.

Course resources


The following is required for the course:

  • T. Ba┼čar, S. P. Meyn, W. R. Perkins, Lecture Notes on Control System Theory and Design.

It can be purchased from the ECE Supply Center, 1031 ECE Building. I also recommend bringing these lecture notes to class.

In addition, these textbooks are optional supplements to the material covered in class:

  • C-T. Chen, Linear System Theory and Design. (The most recent is the 4th edition, which I have not seen yet. I've used both the 2nd and 3rd editions of this book, which are both good. The 2nd edition is far more comprehensive, but the 3rd edition is far more user-friendly.)

  • J. P. Hespanha, Linear Systems Theory.

  • R. W. Brockett, Finite Dimensional Linear Systems.

Further reading for the interested student:

  • S. Axler, Linear Algebra Done Right. (This provides a quick undergraduate-level overview of linear algebra.)

  • G. Strang, Linear Algebra and Its Appplications. (This is the standard textbook in linear algebra.)

  • F. M. Callier and C. A. Desoer, Linear System Theory. (Terribly formatted, but very comprehensive coverage of material.)

  • T. Kailath, Linear Systems Theory.

  • W. J. Rugh, Linear System Theory.

  • D. F. Delchamps, State Space and Input-Output Linear Systems.

Additional resources:

Course website

The central hub for this course will be the course website:

This webpage will be maintained and is the best resource for up-to-date information about the course. In the unlikely event of conflicting information, the information on this webpage will take precedence.


This course also has a Piazza:

Official announcements will be done through Piazza. You will be held responsible for content in announcements made on Piazza. MAKE SURE you are: a) enrolled in the course on Piazza, and b) have some method to stay up-to-date with course announcements.

To reiterate: you will be held responsible for content in announcements on Piazza.

And once more for emphasis, with emphasis: you will be held responsible for content in announcements on Piazza.


Grading will be done on Gradescope. The course's entry code is 92DP2W.

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:

I do not expect academic integrity will be an issue, but it is worth discussing briefly. If you find that you are struggling with the material in the course, do not hesitate at all to reach out to me. Send me an email, drop by my office hours, see me after class, post on Piazza, slip a note under my office door, whatever. One should not feel like they must resort to cheating in my class.


  • System modeling and analysis:

    • system design as a control problem - constraints, goals and performance specifications, input-output and state space models

    • linearization

    • review of linear algebra

    • fundamentals of state-space analysis of linear systems

  • System structural properties:

    • stability

    • introduction to Lyapunov methods

    • controllability, observability

    • canonical forms and minimal realizations

    • modeling uncertainties

    • system sensitivity and robustness measures

  • Feedback system design:

    • basic properties of feedback

    • stabilization and eigenvalue placement by state and output feedback

    • disturbance rejection

    • observers for estimating states, and observer feedback systems

  • Optimum feedback control:

    • dynamic programming and the Hamilton-Jacobi-Bellman equation

    • synthesis of optimum state regulator systems

    • numerical methods

  • Introduction to the minimum principle:

    • calculus of variations and necessary conditions for optimal trajectories

    • minimum principle for bounded controls

    • time-optimal control of linear systems

    • numerical methods