ECE 515/ME 540 (Control System Theory and Design) - Spring 2022 - Syllabus

Quick links


  • Entry code: V825XW


Lecture Zoom link:

Office Hours Zoom link:

Note these Zoom links are password-protected; please check your email or send me an email for the password.

Media Space channel: Recorded lectures are available at

Times and places

  • Course lecture: Mondays and Wednesdays at 11:00am – 12:20pm CT in 4070 ECEB and online.

  • Instructor office hours (until Friday, March 25th): Wednesdays at 10:00am – 10:50am CT in 4070 ECEB and online.

  • Instructor office hours (beginning Monday, March 28th): By appointment.

  • TA office hours (until Friday, March 25th): Friday, 10am – 11:30am CT, online only.

  • TA office hours (beginning Monday, March 28th): Wednesday, 5pm – 6:30pm CT, online only.

Course folks

  • Instructor: Roy Dong

    • email: roydong at illinois dot edu

  • TA: Peter Du

  • TA: Eric Liang

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.

Course logistics

The next two sections are Course technologies and Course components. Course technologies outlines which websites and platforms this course will use, and the protocol for interacting with them (e.g. how Zoom will be used). Course components outlines the parts of class and how they will be conducted (e.g. how lectures and homeworks will be run).

Course technologies

The course will use the following technologies: Zoom, Gradescope, and Piazza. This section outlines the details of how each of those technologies will be used.


Lectures will be conducted in-person. For convenience, I will also simulcast them via Zoom. The link is available at the top of the page, under Quick links.

The Zoom link is password-protected. You will receive the password in your email a few days prior to the first lecture, and, barring some additional extenuating circumstances, the password should remain the same throughout the semester.

If you are officially enrolled and have not received the Zoom passwords a day prior to the first lecture, or if you enrolled late and do not have the Zoom password, send an email to the course instructor and TA.

Additionally, there may be circumstances in which lecture must be conducted remotely. In this case, live lectures will be exclusively on Zoom, with recordings uploaded later. I will send out announcements should this occur.


Homework assignments and exams will both be administered via Gradescope. The entry code can be found above, under Quick links.

When you enroll, please use the following information.

  • Email address: Use your email.

  • Student ID #: Use your University Identification Number (UIN), which can be found on your ID card.

Failure to do so may cause your grade to not be correctly entered into the Registrar!

More details of how homeworks and exams will be handled is under Course components.


Piazza will be used to facillitate course discussions.

You are responsible for announcements made via Piazza, which may modify dates and requirements for the course. Almost all announcements will be made via Piazza, although some which aren't public may be made through email instead (e.g. passwords for the Zoom links will be sent via email).

Course components

This course has 4 components: lectures/discussion, readings, homeworks, and exams. Please read below to see the details of each component, and what resources and technologies will be required for participation in the class.



Lectures will take place in-person. Additionally, they will be simulcast via Zoom. The lecture's Zoom link is available at the top of this page, under Quick links.

Recordings of each lecture will be posted online on Media Space. The link to the Media Space channel is available at the top of this page, under Quick links. Lecture recordings should be uploaded by 5pm CT, the day of the lecture. Please send the course instructor an email if the lecture is not available by then.

Attendance is encouraged, but it is understood that circumstances this semester may vary, and some students may not be able to regularly attend the lecture.

Office Hours

Both the course instructor and the TA will hold office hours. The time and location of these office hours can be found above, under Times and places.


Readings will come from the course textbook, T. Başar, S. P. Meyn, W. R. Perkins, Lecture Notes on Control System Theory and Design. This is available online here:

A schedule of assigned readings is available at Course Schedule (which can also be accessed on the menu on the left of this webpage). Students are expected to maintain pace with this schedule of readings.


Homeworks are generally due on Gradescope on Thursdays at 2pm CT, 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.


This course will have two midterm exams, and one final exam. The exact dates will be posted on the Course Schedule (which can also be accessed on the menu on the left of this webpage).

Exam format

All exams will be take-home exams. Exams will be posted on Gradescope by 8pm CT the day prior to the exam. (You can download the exam PDF from Gradescope at that time; I will send a Piazza announcement when the exam is available.) Exams will be collected on Gradescope, and must be submitted by 11:59pm CT, the day of the exam.

You will have a 24-hour window in which to take the exam. Once you download the exam from Gradescope, you will have 3 hours to submit a completed exam. Please allot time to upload the PDF as needed, as the submission must be completed by the end of this time window.

As per the take-home format of the exam, you will need to show your work to receive full credit. (Stating the correct answer without derivation will not receive full credit, for example.)

Exam submission

As for filling out the exam, you have multiple options. If you have a tablet or similar hardware, feel free to load the PDF onto your device and write on it, and then export it to PDF for upload to Gradescope. You may print out the exam, complete it with pen or pencil, and scan it for upload.

If you do not have access to a printer, you may complete the answers on a separate sheet of paper, but the exam may require you to label points on provided plots. Please make sure you allot time to cleanly re-draw any provided plots yourself if you do not have a printer.

Regardless of how you choose to take it, the midterm must be uploaded to Gradescope by the deadline. The exam duration includes time to accommodate any issues you may have in uploading, so please allocate sufficient time to handle any unforeseen circumstances that may delay submission.

Resources during exams

The exam will be open-book, open-note, and open-Internet.

You may not talk to your peers on the class, nor anyone else about this exam during the exam time. You may not ask questions anywhere on the Internet related to this exam either. For example, you may read existing Stack Exchange questions and answers, but you may not ask a new question on Stack Exchange.


The grades will be broken down as follows.

homeworks 40%
midterm exam 1 20%
midterm exam 2 20%
final exam 20%

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


The following is required for the course:

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.

  • B. Rynne and M. A. Youngson, Linear Functional Analysis.

Additional resources:

Course website

The central hub for this course will be the course website. You are currently here.

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. The link is available at the top of this page, under Quick links.

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.

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

College-Wide Syllabi Information

The following text is standardized across all syllabi in the Grainger College of Engineering. This class stands behind and upholds the following statements and values therein.

Sexual Misconduct Reporting Obligation

The University of Illinois is committed to combating sexual misconduct. Faculty and staff members are required to report any instances of sexual misconduct to the University’s Title IX Office. In turn, an individual with the Title IX Office will provide information about rights and options, including accommodations, support services, the campus disciplinary process, and law enforcement options.

A list of the designated University employees who, as counselors, confidential advisors, and medical professionals, do not have this reporting responsibility and can maintain confidentiality, can be found here:

Other information about resources and reporting is available here:

Academic Integrity

The University of Illinois at Urbana-Champaign Student Code should also be considered as a part of this syllabus. Students should pay particular attention to Article 1, Part 4: Academic Integrity. Read the Code at the following URL:

Academic dishonesty may result in a failing grade. Every student is expected to review and abide by the Academic Integrity Policy: Ignorance is not an excuse for any academic dishonesty. It is your responsibility to read this policy to avoid any misunderstanding. Do not hesitate to ask the instructor(s) if you are ever in doubt about what constitutes plagiarism, cheating, or any other breach of academic integrity.

Religious Observances

Illinois law requires the University to reasonably accommodate its students’ religious beliefs, observances, and practices in regard to admissions, class attendance, and the scheduling of examinations and work requirements. You should examine this syllabus at the beginning of the semester for potential conflicts between course deadlines and any of your religious observances. If a conflict exists, you should notify your instructor of the conflict and follow the procedure at to request appropriate accommodations. This should be done in the first two weeks of classes.

Disability-Related Accommodations

To obtain disability-related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the Disability Resources and Educational Services (DRES) as soon as possible. To contact DRES, you may visit 1207 S. Oak St., Champaign, call 333-4603, e-mail or go to If you are concerned you have a disability-related condition that is impacting your academic progress, there are academic screening appointments available that can help diagnosis a previously undiagnosed disability. You may access these by visiting the DRES website and selecting “Request an Academic Screening” at the bottom of the page.

Family Educational Rights and Privacy Act (FERPA)

Any student who has suppressed their directory information pursuant to Family Educational Rights and Privacy Act (FERPA) should self-identify to the instructor to ensure protection of the privacy of their attendance in this course. See for more information on FERPA.

Anti-Racism and Inclusivity Statement for Inclusion in Course Syllabi

The intent is to raise student and instructor awareness of the ongoing threat of bias and racism and of the need to take personal responsibility in creating an inclusive learning environment.

The Grainger College of Engineering is committed to the creation of an anti-racist, inclusive community that welcomes diversity along a number of dimensions, including, but not limited to, race, ethnicity and national origins, gender and gender identity, sexuality, disability status, class, age, or religious beliefs. The College recognizes that we are learning together in the midst of the Black Lives Matter movement, that Black, Hispanic, and Indigenous voices and contributions have largely either been excluded from, or not recognized in, science and engineering, and that both overt racism and micro-aggressions threaten the well-being of our students and our university community.

The effectiveness of this course is dependent upon each of us to create a safe and encouraging learning environment that allows for the open exchange of ideas while also ensuring equitable opportunities and respect for all of us. Everyone is expected to help establish and maintain an environment where students, staff, and faculty can contribute without fear of personal ridicule, or intolerant or offensive language. If you witness or experience racism, discrimination, micro-aggressions, or other offensive behavior, you are encouraged to bring this to the attention of the course director if you feel comfortable. You can also report these behaviors to the Bias Assessment and Response Team (BART) ( Based on your report, BART members will follow up and reach out to students to make sure they have the support they need to be healthy and safe. If the reported behavior also violates university policy, staff in the Office for Student Conflict Resolution may respond as well and will take appropriate action.