University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
EECS221A
Linear System Theory
Fall Semester 2020
Course information:
UCB OnLine Course Catalog and Schedule of Classes
Lecture Information: TuTh 9:3011 am PST, remote instruction. Link in bcourses calendar.
Discussion Section Information: Fri 10am12pm PST, remote instruction. Link in bcourses calendar.
Midterm Information: The midterm test will be on Th Oct 8, during class time.
Instructor

Claire Tomlin
tomlin at berkeley.edu
Office hours: Tu, Wed: 11 am  12 pm PST, link in bcourses calendar
Teaching Assistant

Jaimie Swartz
jaimie.swartz at berkeley.edu
Office hours: Mon, Wed: 1  2 pm PST, link in bcourses calendar
Course Description
This course provides an introduction to the modern state space theory of linear systems for students of circuits, communications, controls, and signal processing. In some sense it is a second course in linear systems, since it builds on an understanding that students have seen linear systems in use in at least some context before. The course is on the one hand quite classical and develops some rather well developed material, but on the other hand is quite modern and topical in that it provides a sense of the new vistas in embedded systems, computer vision, hybrid systems, distributed control, game theory and other current areas of strong research activity.
Topics include:
 A review of linear algebra and matrix theory. The solutions of linear equations.
 Leastsquares approximation, linear programming, singular value decomposition and principal component analysis.
 Linear ordinary differential equations: existence and uniqueness of solutions, the statetransition matrix and matrix exponential.
 Numerical considerations: matrix sensitivity and condition number, numerical solutions to ordinary differential equations, and stiffness.
 Inputoutput and internal stability; the method of Lyapunov.
 Controllability and observability; basic realization theory.
 Control and observer design: pole placement, state estimation.
 Linear quadratic optimal control: Riccati equation, properties of the LQ regulator and Kalman filtering.
 Advanced topics such as robust control, hybrid system theory, linear quadratic games and distributed control will be presented based on allowable time and interest from the class.
It is recommended that students have previously taken a linear algebra course (MATH 110 or equivalent).
Handouts and Lecture Notes
Recorded Lectures
 08/27 Lecture 1 video, board notes
 09/01 Lecture 2 video, board notes
 09/03 Lecture 3 video, board notes
 09/08 Lecture 4 video, board notes
 09/10 Lecture 5 video, board notes
 09/15 Lecture 6 video, board notes
 09/17 Lecture 7 video, board notes
 09/22 Lecture 8 video, board notes
 09/24 Lecture 9 video, board notes
 09/29 Lecture 10 video, board notes
 10/01 Lecture 11 video, board notes
 10/06 Lecture 12 video, board notes
 10/14 Lecture 13 video, board notes
 10/15 Lecture 14 video, board notes
 10/20 Lecture 15 video, board notes
 10/22 Lecture 16 video, board notes
 10/27 Lecture 17 video, board notes
 10/29 Lecture 18 video, board notes
 11/03 Lecture 19 video, board notes
 11/05 Lecture 20 video, board notes
 11/10 Lecture 21 video, board notes
 11/12 Lecture 22 video, board notes
 11/17 Lecture 23 video, board notes
 11/19 Lecture 24 video, board notes
 11/24 Lecture 25 video, board notes
 12/1 Lecture 26 video, board notes
 12/3 Lecture 27 video, board notes
 12/3 Video Instructions for Course Evaluation As per HKN Guidance, if more than 80% of the class fills in the evaluations, everyone in the class will receive extra credit towards their course grade!
Homework
Discussion
 08/28
Discussion 1,
Video Recording,
Solutions
 09/4 Discussion 2
Video Recording,
Solutions
 09/11 Discussion 3
Video Recording,
Solutions
 09/18 Discussion 4
Video Recording,
Solutions
 09/25 Discussion 5
Video Recording,
Solutions
 10/2 Discussion 6
Video Recording,
Solutions
 10/16 Discussion 7
Video Recording,
Solutions
 10/23 Discussion 8 (includes sample code for HW6#2!)
Video Recording,
Solutions
 10/30 Discussion 9
Video Recording,
Solutions
 11/6 Discussion 10
Video Recording,
Solutions
 11/13 Discussion 11
Video Recording,
Solutions
 11/20 Discussion 12
Video Recording,
Solutions
 12/04 Discussion 13
Video Recording,
Solutions
 12/11 Final Exam review session video recording,
Markup of F19 exam solutions
Links
Grading
Homework 40%, there will be (roughly) 10 problem sets
Midterm 20%, in class
Final 40%
Recommended Reading
Systems:
 F. Callier & C. A. Desoer, Linear System Theory, SpringerVerlag, 1991.
 C.T. Chen, Linear Systems Theory and Design, Holt, Rinehart & Winston, 1999.
 T. Kailath, Linear Systems Theory, PrenticeHall.
 R. Brockett, Finitedimensional Linear Systems, Wiley.
 W. J. Rugh, Linear System Theory, PrenticeHall, 1996.
 D. F. Delchamps, State Space and InputOutput Linear Systems,
Springer Verlag, 1988.
Algebra:
 G. Golub and C. Van Loan, Matrix Computations, Johns Hopkins Press.
 M. Gantmacher, Theory of Matrices, Vol 1 & 2, Chelsea.
 G. Strang, Linear Algebra and its Applications, 3rd edition, 1988.
 G. Strang, Introduction to Linear Algebra, 4th ed., WellesleyCambridge Press, 2009.
Analysis:
 J. Hale, Ordinary Differential Equations, Wiley.
 W. Rudin, Principles of Mathematical Analysis, McgrawHill.
 W. Rudin, Real and Complex Analysis, McgrawHill.
 B. Rynne and M.A. Youngson, Linear Functional Analysis, Springer, 2007.