CDS 212 Fall 2011

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Feedback Control Theory


  • John Doyle,
  • Lectures: Tu/Th, 2:30-4 pm, 314 Annenberg

Teaching Assistants

  • Na (Lina) Li,
  • Office hours: Wed, 3:00-4:00pm, 230 Annen

Course Description

Introduction to modern feedback control theory with emphasis on the role of feedback in overall system analysis and design. Examples drawn from throughout engineering and science. Open versus closed loop control. State-space methods, time and frequency domain, stability and stabilization, realization theory. Time-varying and nonlinear models. Uncertainty and robustness.


Reading materials:

Please read Megretskich8 and RantzerKYP; others are more adavanced

Other materials: A Fundamental Limit on the Robustness of Complex Systems

  • 13 Oct 2011: Notes from lecture: Chapter 4 Chapter 6
  • 6 Oct 2011: Today's class: 2:00pm-3:00pm, 107 Annen

Reading materials: Internal model principle


The two primary texts for the course (available via the online bookstore) are

 [DFT]  J. Doyle, B. Francis and A. Tannenbaum, Feedback Control Theory, Dover, 2009 (originally published by Macmillan, 1992). Available online at
 [DP]  G. Dullerud and F. Paganini, A Course in Robust Control Theory, Springer, 2000.

The following additional texts may be useful for some students:

 [FBS]  K. J. Astrom and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Available online at

Lecture Schedule

Week Date Trunk Reading Homework
1 27 Sep 
29 Sep
  • Norms for signals and systems
DFT Ch 1, 2 
DP Ch 3
2 4 Oct
6 Oct
  • Feedback, stability and performance
DFT Ch 3
(FBS 9.1-9.3)
(FBS 11.1-11.2)
3 11 Oct
13 Oct
  • Uncertainty and robustness
DFT Ch 4
(FBS 12.1‑12.3)
4 18 Oct
20 Oct
  • Fundamental limits
DFT Ch 6
(FBS 11.4, 12.4)
5 25 Oct
27 Oct
  • Fundamental limits in control and information theory
  • Realization theory, controllability, observability
  • Lyapunov equation and stability conditions
DP Ch 2 ,4
6 1 Nov
3 Nov
  • LMIs
  • Model reduction
DP Ch 2,4
SDP Duality and LTI
LMIs Ch 2
7 8 Nov
10 Nov
  • SDP duality for LTI
  • H2 optimal control
DP Ch 5, 6
SDP Duality and LTI

15 Nov
17 Nov
22 Nov
  • H2 synthesis by SDP
  • KYP Lemma
  • MIMO
  • Model Uncertainty
  • SOS
DP Ch 6, 7 , 8
10 29 Nov
1 Dec
  • Studying the Logistic Map and the Mandelbrot Set using SOS Methods
  • System identification
  • Heart rate variability


The final grade will be based on homework: There will be 9 one-week problem sets, due each Thursday by 5pm in the TA's mailbox on the third floor of Annenberg. Each student may hand in at most one homework late (no more than 5 days).

The lowest homework score you receive will be dropped in computing your homework average. In addition, if your score on the final is higher than the weighted average of your homework and final, your final will be used to determine your course grade.

Collaboration Policy

Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course is not allowed. All solutions that are handed should reflect your understanding of the subject matter at the time of writing.

Additional References (Optional)