CDS 131, Fall 2020
Linear Systems Theory  
Instructors

Teaching Assistants

This is the course homepage for CDS 131, Fall 2020. This course is intended for first year graduate students in controls, advanced undergraduates in EE, ChE, and ME who have taken a basic controls course (e.g., CDS 110, ChE 105, EE 113), and motivated graduate students in other disciplines would would like to learn more about linear systems and control. All students taking the course should also have a good understanding of (matrix) differential equations and linear algebra, in addition to some familiarity with control system design.
Access information[edit]
 Lectures (Zoom): MWF, 23 pm. See Caltech Canvas for Zoom link (registered students only)
 Lecture recordings (Google Drive): See Caltech Canvas for link (registered students only)
 Class discussion (Piazza): See Caltech Canvas for Piazza link (registered students only)
Catalog Description[edit]
CDS 131. Linear Systems Theory. 9 units (306); first term. Prerequisites: Ma 1b, Ma 2, ACM/IDS 104 or equivalent (may be taken concurrently). Basic system concepts; statespace and I/O representation. Properties of linear systems, including stability, performance, robustness. Reachability, observability, minimality, state and outputfeedback. Instructor: Murray.
Lecture Schedule[edit]There will be 23 one hour lectures per week, with the specific days varying from weektoweek. The lecture days for each week will be announced in class and posted here at least 1 week in advance. Reading:

Announcements[edit]

Date  Topic  Reading  Homework 
Week 1 30 Sep 
Introduction and review


HW #1 Out: 30 Sep 
Week 2 5 Oct 
Linear I/O systems


HW #2 Out: 7 Oct 
Week 3 12 Oct 
Reachability


HW #3 Out: 14 Oct 
Week 4 19 Oct 
State feedback


HW #4 Out: 21 Oct 
Week 5 26 Oct 
Observability and state estimation


HW #5 Out: 28 Oct 
Week 6 2 Nov 
Signals and Systems


HW #6 Out: 4 Nov 
Week 7 9 Nov 
Frequency domain analysis


HW #7 Out: 11 Nov 
Week 8 16 Nov 
Uncertainty and robustness


HW #8 Out: 18 Nov 
Week 9 23 Nov 
Fundamental limits


HW #9 Out: 25 Nov 
Week 10 2 Dec 
Review for final  Final Out: 4 Dec

Grading[edit]
The final grade will be based on homework sets, a midterm exam, and a final exam:
 Homework (70%): Homework sets will be handed out weekly and due on Wednesdays by 2 pm using GradeScope. Each student is allowed up to two extensions of no more than 2 days each over the course of the term. Homework turned in after Friday at 2 pm or after the two extensions are exhausted will not be accepted without a note from the health center or the Dean. MATLAB/Python code and SIMULINK/Modelica diagrams are considered part of your solution and should be printed and turned in with the problem set (whether the problem asks for it or not).
 The lowest homework set grade will be dropped when computing your final grade.
 Final exam (30%): The final exam will be handed out on the last day of class (4 Dec) and due at the end of finals week. It will be an open book exam and computers will be allowed (though not required).
Collaboration Policy[edit]
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor, but you cannot consult homework solutions from prior years and you must cite any use of material from outside references. 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. Any computer code that is used to solve homework problems is considered part of your writeup and should be done individually (you can share ideas, but not code).
No collaboration is allowed on the final exam.
Course Text and References[edit]
The primary course texts are
 [FBS2e] K. J. Astrom and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, Second Edition*, 2020.
 [FBS2s] Richard M. Murray, Feedback Systems: Notes on Linear Systems Theory, 2020. (Updated 30 Oct 2020)
 [DFT] J. Doyle, B. Francis and A. Tannenbaum, Feedback Control Theory, Dover, 2009 (originally published by Macmillan, 1992).
 [OBC] R. M. Murray, "OptimizationBased Control", 2010. Online access
 [Son98] E. D. Sontag, Mathematical Control Theory, Springer, 1998. Online access
* Please make sure to use the second edition [FBS2e].
The following additional references may also be useful:
 [Lew03] A. D. Lewis, A Mathematical Approach to Classical Control, 2003. Online access.
Note: the only sources listed here are those that allow free access to online versions. Additional textbooks that are not freely available can be obtained from the library.