University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
EECS221A
Linear System Theory
Fall Semester 2019
Course information:
UCB OnLine Course Catalog and Schedule of Classes
Lecture Information: TuTh 9:3011am, Bechtel 240
Section Information: Fri 24pm, Cory 241
Instructor

Claire Tomlin
721 Sutardja Dai Hall
tomlin at eecs.berkeley.edu
Office hours: Tu, Wed: 11am  12pm
Teaching Assistant

Andrea Bajcsy
750 Sutardja Dai Hall
abajcsy at eecs.berkeley.edu
Office hours: Mon, Wed: 2  3pm (Cory 504)
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
Homework
Discussion
08/26 Section 1 (08/30)
09/2 Section 2 (09/06)
09/9 Section 3 (09/13)
09/16 Section 4 (09/20)
09/23 Section 5 (09/24)
09/30 Section 6 (10/04)
10/07 Section 7 (10/11)
10/11 Midterm Review and Recap
10/14 Section 8 (10/18)
10/21 Section 9 (10/25)
10/28 Section 10 (11/1)
11/4 Section 11 (11/8)
11/11 Section 12 (11/15)
12/02 Section 13 (12/06)
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.