ECE 550: Linear Systems Theory and Design (Spring 2022)

Lectures

Tue/Thu, 3:30-4:45pm, LH 312 (Lincoln Hall)
Until in-person instruction is resumed, the course will be taught online in Blackboard Collaborate Ultra.

Instructor

Shuo Han (hanshuo@uic.edu)
Office hours: Tue, 1:30-3:00pm, 1110 SEO
Until in-person instruction is resumed, office hours will be held online (by appointment only, see instructions).

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
  • Stabilization using feedback: Reachability/controllability and observability, pole placement, separation principle
• Part 2: Connecting state space and frequency domain
  • Realization theory
  • Signal and system norms
• Part 3: Performance and robustness
  • Modeling uncertainties
  • Performance limits
  • H₂ and H_∞ control
  • Controller design under uncertainties: Introduction to robust control

Course Policy

Grading

• Homework (20%): Homework sets are issued every Thursday and are due the following Thursday in class.
  • 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).
• Incomplete grades are given according to the UIC policy. For this course, "satisfactory progress" means you have scored at least 50% in the midterm exam.
• Guaranteed cutoff grades: A-85%, B-70%, C-55%.

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: lectures and recordings, viewing grades
• Piazza: course announcements, downloading problem sets and course materials, Q&A

Homework Policy

• You are required to submit a hardcopy your homework in class. If you are unable to attend the lecture, you need to email me at least one day prior to the due date for approval of electronic submission (usually I will say yes unless you are doing it many times), after which you can email your homework to me by the due date. If you are writing your solution by hand, we recommend that you digitize it using a high-quality scanner (as opposed to taking photos), which is available and free at the Daley Library. This ensures that your writing remains legible after we print out your electronic submission.
• Make a copy of your homework prior to submission. You will be asked to provide your copy for any claims of missing homework.
• 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, make sure the submitted copy is legible.
• You may consult the lecture notes, the textbook 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. You cannot consult homework solutions from prior years or solution manuals.
• Show all your work to receive credits. However, we will deduct points from long needlessly complex solutions, even if they are correct. 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 without proper supporting documents (e.g., a note from doctor or the Dean).

Collaboration

• Collaboration on homework assignments is encouraged. All solutions that are handed in should be written up individually and should reflect your own understanding of the subject matter at the time of writing. 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 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,

COVID-19 Special Policies

Please read carefully the official guidance provided by the University.

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 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.

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 that 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