Linear Feedback Control


  • We are back to classroom teaching/learning, although part of the lectures will still be provided remotely
  • Each week, slides and/or videos will be uploaded
  • Grading will be based on one (1) final project & report

Learning Objectives:

  • Study how to model linear systems using state-space models;
  • learn fundamental system properties: stability, controllability, observability;
  • design feedback controllers for linear systems.


  • Prof. Kai Cai (Engineering Building F-610)
  • Email:
  • Office hour: anytime appointment by email

Lecture Schedule:

  • Period: Sep. 2023 -- Jan. 2024
  • Day and Time: Tuesdays 13:15-14:45

Textbook / Reference:

Lecture notes in class will cover all contents. Two excellent references are:

  1. B.A. Francis, "Systems Control", lecture notes, Department of Electrical and Computer Engineering, University of Toronto, 2008. (PDF posted for study purpose: part1, part2, part3, ECE557_part4.pdf, part5, part6)
  2. J.P. Hespanha, " Linear Systems Theory", Princeton University Press, 2009. (Copies to be lent by request)


Matlab (download the Windows 64bit version here, with university campus license). After installing the software, you also need to make a change according this document.


Linear Algebra, Introduction to Control Engineering

Course Outline:

    Dates              Topics
  1. 2023.09.26 Introduction (+ self-review of state models and linearization)
  2. 2023.10.03 Stability concepts: Lyapunov & asymptotic stability
  3. 2023.10.10 Initial value problem of ordinary differential equations
  4. 2023.10.17 Matrix exponential: diagnolizable case
  5. 2023.10.24 Matrix exponential: nondiagnolizable case
  6. 2023.10.31 Stability criteria
  7. 2023.11.07 Controllability
  8. 2023.11.14 State-feedback control
  9. 2023.11.28 Eigenvalue assignment
  10. 2023.12.05 Stabilizability
  11. 2023.12.12 Observability
  12. 2023.12.19 Kalman decomposition
  13. 2024.01.09 Output-feedback control
  14. 2024.01.16 Reference tracking
  15. 2024.01.23 Optimal control