ECE 550: Linear Systems Theory and Design (Spring 2026)

Lectures

Mon/Wed, 3:00-4:15pm, LH 120 (Lincoln Hall)

Instructor

Shuo Han (hanshuo@uic.edu)
Office hours: Mon/Wed, 2:00-2:45pm, 1110 SEO

Grader

N/A

Course Description

This graduate-level course focuses on modeling, analysis, and design of linear dynamical systems in state space. The course will help build up the foundation for students to read literature and learn other advanced topics in control.

Prerequisites

ECE 350 or equivalent course on introductory control. Linear algebra. Familiarity with MATLAB.

Topics

• Part 1: State space fundamentals
  • State-space modeling
  • Stability: Internal stability (Lyapunov stability) and input-output stability
• Part 2: Basic controller design in state space
  • Reachability/controllability and observability
  • Stabilization using feedback: pole placement, separation principle
• Part 3: Controller design for robustness and performance
  • Realization theory
  • Signal and system norms
  • Modeling uncertainties
  • Controller design under uncertainties: Introduction to robust control
  • Performance limits

Course Policy

Grading

• Homework (20%): Homework sets are issued every Wednesday and are due 8pm the following Wednesday.
  • Homework will be graded on a scale from 0 to 4 based on effort and completion.
  • The lowest one will be dropped towards calculating your total homework grade. Namely, if there are X homework sets in total, then the best X-1 sets will be used.
  • There will be about 12 homework sets in total.
  • No homework will be assigned in Weeks 1, 8 (due to the midterm exam), and 15 (due to the final exam).
• Midterm (35%) and final (45%) exams: Both will be in-class, closed-book, and closed-notes. The dates will be announced at a later time. You may use a single handwritten letter-sized double-sided "cheat sheet" during the midterm exam and two for the final exam. The cheat sheet(s) may contain formulas, facts, definitions, and theorems. However, your cheat sheet(s) may not contain worked examples. You must hand in your cheat sheet(s) along with your completed exam. No calculators/computers are allowed in the exams.
  
• There will be no make-up exams or substitutions (e.g., course projects).
• Guaranteed cutoff grades: A-85%, B-70%, C-55%.
• Incomplete grades are given according to the UIC policy. For this course, "satisfactory progress" means that you are currently receiving a grade of C or better at the time of requesting an incomplete grade.

Course Logistics

We will use a number of websites/apps throughout this course, each of which has a different purpose.

• This website: course syllabus
• UIC Blackboard: viewing grades
• Piazza: course announcements, downloading problem sets and course materials, Q&A
• Gradescope: submitting homework

Homework Policy

• You are required to submit your homework on Gradescope. You are encouraged (but not required) to typeset your homework using LaTeX. See the section "LaTeX resources" on this page if you are new to LaTeX. If you choose to write your solution by hand, we ask that you digitize it using a high-quality scanner (as opposed to taking photos), which is available and free at the Daley Library. This will ensure that the submitted copy is legible.
• All solutions handed in should be written up individually and reflect your own understanding of the subject matter at the time of writing. You may consult the lecture notes, the textbooks listed below, references mentioned in class, other students (see the "Collaboration" section below), or the instructor. You may also consult outside references not listed on the course webpage, provided that you cite those references in your homework solutions. This includes the use of online forums and generative AI. You cannot consult homework solutions from prior years or solution manuals.
• Show all your work to receive credits. We prefer correct and concise solutions. If you find that your solution to a problem goes on and on for many pages, you should try to come up with a simpler one. One useful way to shorten your solutions is to cite results derived in class or from the textbooks.
• Late homework: Late homework will not be accepted in any circumstances. The policy of dropping the lowest grade in homework assignments is meant to cover emergencies. Use it wisely.

Collaboration

• Collaboration on homework assignments is encouraged. Notes taken during the discussions cannot be used at the time of writing your own solutions.
• MATLAB scripts and plots are considered part of your writeup and should be done individually (you can share ideas, but not code).
  
• If you have collaborated with others, include their names and the problems that you have collaborated on, and to what extent. Also, be explicit that you have written your solution on your own and that you have not shared code. No statement will be treated as no collaboration.
  • Example: "I collaborated with [names] on Problems 1 and 3, discussing related concepts and solution strategies. The solutions that I submit reflect my own understanding at the time of writing. I have not shared my code with others."

Academic Integrity

• We treat academic dishonesty seriously. All offenses are reportable to the University.
• For any violation of the course policy in homework, the homework assignment will receive a grade of zero, and a warning will be issued to the offender. For homework assignments, the zero grade will not be dropped in the calculation of the letter grade.
• For two violations of the course policy, the final letter grade of the offender will be lowered by one tier, e.g., from A to B.
• For more than two violations of the course policy, the offender will receive a letter grade of F.
• The penalty applies to all parties involved.
• You can read this page by Jeff Erickson (UIUC) to learn more about academic integrity,

Others

• You should keep the course material (lecture notes, recordings, and homework problems and solutions) for personal use only and not post them on public websites (e.g., Course Hero).
• Students who wish to observe their religious holidays should notify the instructor by the tenth day of the semester of the date when they will be absent unless the religious holiday is observed on or before the tenth day of the semester. In such cases, the students should notify the instructor at least five days in advance of the date when he/she will be absent. Every reasonable effort will be made to honor the request.
• UIC is committed to full inclusion and participation of people with disabilities in all aspects of university life. To receive accommodations, you will need to disclose the disability to the Disability Resource Center (DRC), complete an interactive registration process with the DRC, and provide me with a Letter of Accommodation (LOA). Upon receipt of an LOA, I will gladly work with you and the DRC to implement approved accommodations.

Course Text and References

There is no single textbook that covers all the topics in this course. The lecture notes will be the primary source of reference.

The recommended main textbook for the course is:

• [Hes18] João P. Hespanha, Linear Systems Theory, 2nd edition, Princeton University Press, 2018. UIC access Errata
  • If you are using the e-book, close the browser tab once you finish so thact others can read it.
  • A hardcopy of the book is on reserve at the Daley library (2-hour loan period).

Other references

Control theory:

• [Bay99] John S. Bay, Fundamentals of Linear State Space Systems, 1999. Online access
• [AM08] K. J. Astrom and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Online access (2nd edition)
• [DFT] J. Doyle, B. Francis, and A. Tannenbaum, Feedback Control Theory, Dover, 2009 (originally published by Macmillan, 1992). Online access
• [DP05] Geir E. Dullerud and Fernando Paganini, A Course in Robust Control Theory: A Convex Approach, Springer, 2005. UIC access
• [WL07] Robert L. Williams II and Douglas A. Lawrence, Linear State-Space Control Systems, Wiley, 2007. UIC access
• [AM07] Panos J. Antsaklis and Anthony N. Michel, A Linear Systems Primer, Springer, 2007. UIC access

Linear algebra:

• Sheldon Axler, Linear Algebra Done Right, Springer, 2015. UIC access
• Géza Schay, A Concise Introduction to Linear Algebra, Springer, 2012. UIC access (Note: The odd-numbered exercises have solutions available in the Solutions Manual for Students on the book's webpage.)

Classical control theory:

• G. F. Franklin, J. D. Powell, and A. Emami-Naeni, Feedback Control of Dynamic Systems, Prentice Hall, 2005.

Note: For textbooks with "UIC access", you need to connect to UIC campus network or VPN. Alternatively, you can search for the textbook on the UIC library website and click the eBook link therein.

LaTeX Resources

• Installation: See a list of LaTeX distributions for common operating systems.
• LaTeX editors
  • Because the LaTeX source files are in plain text, you can always use your favorite text editor.
  • For a WYSIWYG document processor (similar to MS Word) based on LaTeX: LyX
  • Alternatively, you can use an online browser-based LaTeX editor: Overleaf
• LaTeX usage
  • If you are new to LaTeX, the best way to begin is by typesetting using an existing template. You can find a LaTeX template useful for this course on this page. Read template_notes.pdf and use template_notes.tex as a start.
  • For how to compile a PDF from LaTeX source, see this page. We recommend using pdfLaTeX.
  • If you do not know how to type a mathematical symbol, you can get help from Detexify.
  • Comprehensive usage guides are available on the following websites:
    • Overleaf LaTeX documentation
    • Wikibooks LaTeX guide