AE 6531: Aerospace Robust Control

Georgia Tech, Spring Term, 2011

Professor Eric Feron



Lecture notes, all borrowed from Stephen Boyd (and improved from place to place)

  1. Multi-Input, Multi-Output Linear Systems
  2. A controllability form, Hankel matrices, MacMillan degree
  3. Multi-input State-Feedback, Wonham’s Lemma  -  A page correctionFeron’s view of Wonham’s Lemma
  4. Linear quadratic regulator: Discrete-time finite horizon
  5. LQR via Lagrange multipliers
  6. Infinite horizon LQR
  7. Continuous-time LQR
  8. LQR properties: robustness and symmetric root-locus
  9. Invariant subspaces 
  10. Estimation
  11. Optimum linear filters “without the math”
  12. The Kalman filter
  13. The extended Kalman filter
  14. Continuous-time filtering
  15. Observer-based controllers
  16. Basic Feedback System; Stability, transfer matrices and hidden modes
  17. Stability via transfer matrices, loop gain vs sensitivity
  18. Introduction to singular value decomposition
  19. Applications of singular value decomposition
  20. Stabilizing compensators, Q-parameterization for stable plants
  21. Robustness; Q-parameterization for unstable SISO plants
  22. SISO Linear system design via Q-parameterization
  23. Smith, Smith-McMillan Forms, MIMO poles and zeros
  24. Conservation and dissipation
  25. Basic Lyapunov theory
  26. Linear quadratic Lyapunov theory
  27. Lyapunov theory with inputs and outputs
  28. Linear matrix inequalities and the S-procedure
  29. Analysis of systems with sector nonlinearities





Homework 1: –  01/31

Hyun Choi / Daniel Magree

Homework 2:  02/07

Nuno Bacahlau/ Timo Cazenave

Homework 3: - 02/14

Demyan Lantukh / Joshua Ross

Homework 4, -02/21

Thomas Herrman / Gerardo De la Torre

Homework 5, -02/28

Sean Culpepper / Gerardo De la Torre

Homework 6, -03/07

Thomas Herrmann / ?

Homework 7, -03/14

Romain Jobredeaux / Aude Marzuoli

Homework 8, -03/28

Nuno Bacahlau/ Timo Cazenave

Homework 9 -04/04

Demyan Lantukh / Joshua Ross

Homework 10, -04/11

Hyun Choi / Daniel Magree

Homework 11, -04/18


Homework 12, -04/25





Midterm solutions (at least some) here

scilab script for second problem here

Matlab files

Matlab files you'll need for homework assignments and exams.


There is no textbook or reader; the lecture notes cover everything you need. But if you'd like to look at some other texts covering the same topics, we've listed some references below. Good reference material is available online, and can be found using google or wikipedia.

  • A very good general reference that covers several of the topics is Introduction to Dynamic Systems, Luenberger, Wiley.
  • LQR and Kalman filtering are covered in many books on linear systems, optimal control, and optimization. One good one is Dynamic Programming and Optimal Control, vol. 1, Bertsekas, Athena Scientific. Another is Linear Optimal Control, Anderson & Moore, Prentice-Hall.
  • Lyapunov theory is covered in many texts on linear systems, e.g., Linear Systems, Antsaklis & Michel, McGraw-Hill. Nonlinear Lyapunov theory is covered in most texts on nonlinear system analysis, e.g., Nonlinear systems: Analysis, Stability, and Control, Sastry, Springer-Verlag, or Nonlinear Systems Analysis (2nd edition), Vidyasagar, SIAM.
  • Lots of material on LMIs can be found in Boyd, El Ghaoui, Feron, and Balakrishnan, Linear Matrix Inequalities in System and Control Theory, but this is not a book for casual browsing.

Basic course info

Instructor: Eric Feron, MK 419, 404 894 3062, feron(at)gatech(dot)edu

Lectures hours: MWF 10:05-10:55 in Guggenheim 246.

Administrative assistant: Vivian Robinson O’Neal – room MK 421.

Teaching assistants: None

Course requirements: ~weekly homework (10%), midterm (30%), final (60%). Some require some Matlab (or equivalent) programming (not for the exams, though).

Prerequisites: ECE 6550 or equivalent, basic probability and statistics.