CDS 212 Fall 2010

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Feedback Control Theory


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

Teaching Assistants

  • Somayeh Sojoudi,
  • Richard Murray,

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.



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 Branch
1 28 Sep 
30 Sep
Norms for signals and systems DFT Ch 1, 2 
DP Ch 3
HW 1
2 5 Oct+
7 Oct
Feedback, stability and performance DFT Ch 3
(FBS 9.1-9.3)
(FBS 11.1-11.2)
HW 2
  • 6 Oct: Mung Chiang (Princeton), An Axiomatic Theory of Fairness
  • 6 Oct: Mung Chiang (Princeton), Can Random Access Be Optimal?
3 12 Oct+
14 Oct+
Uncertainty and robustness DFT Ch 4
(FBS 12.1‑12.3)
HW 3
  • 12 Oct: Raff D'Andrea (ETHZ), Some applications of distributed estimation and control
4 19 Oct
21 Oct+
  • Fundamental limits
  • Realization theory, controllability, observability
DFT Ch 6
(FBS 11.4, 12.4),
DP Ch 2, 4
HW 4
5 26 Oct+
28 Oct*
  • Lyapunov equation and stability conditions
  • LMIs
DP Ch 4
LMIs Ch 2
HW 5
6 2 Nov*
4 Nov*
  • KYP lemma
  • Model reduction
DP Ch 4,7
HW 6
  • Keith Glover
    • Model reduction
    • Loop shaping
7 9 Nov
11 Nov
  • Uncertain systems
  • MIMO robust control, Convex optimization
DP Ch 8
HW 7
8 16 Nov+
18 Nov
  • Stability of nonlinear systems
  • Sum-of-squares
FBS Ch 4
HW 8
  • IPAM: robust optimization
9 23 Nov+
  • Pablo Parrilo?
10 30 Nov
2 Dec
Links with nformation theory and statistical mechanics HW 9
  • IPAM: applications of optimization


The final grade will be based on homework and a final exam:

  • Homework (75%) - 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).
  • Final exam (25%) - The final will be handed out the last day of class and is due back at the end of finals week. Open book, time limit to be decided (likely N hours over a 4-8N hour period).

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.

No collaboration is allowed on the final exam.

Additional References (Optional)

Date Reading
28 Sep  AldersonDoyle-tsmca (Paper),Glycolysis (Paper), SuppInfo, 1NetCmplxIntro (Slides)
5 Oct  layering (Slides)
19 Oct  BioMetabModeling (Slides),Glycolysis (Paper),Figures,Chap6 (Slides)

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