University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
EE222
Nonlinear Systems: Analysis, Stability, and Control
Spring Semester 2017
Course information:
UCB OnLine Course Catalog and Schedule of Classes
Lecture Information: TuTh 1112:30, 241 Cory.
Discussion Information: Fr 45, 521 Cory (Hogan Room).
Instructor

Professor Claire J. Tomlin,
721 SD Hall

tomlin at eecs.berkeley.edu

http://www.eecs.berkeley.edu/~tomlin

Office hours: Tu 12, Wed 1112
Teaching Assistant

Datong Paul Zhou,
307 Cory Hall

datong.zhou at berkeley.edu

http://people.eecs.berkeley.edu/~datong.zhou/

Office hours: Mon 23, Wed 45, Cory 212
Announcements
 5/8: No office hours this week.
 4/21: Lecture today 45pm.
 3/27: No office hours 3/27 and 3/29.
 3/27: There will be no discussion this Friday, 3/31.
 3/16: There will be no discussion this Friday, 3/17.
 3/10: Solutions to Problem Set 6 have been posted.
 3/9: Solutions to Problem Set 5 have been posted.
 3/1: Solutions to Problem Set 4 have been posted.
 2/19: No office hour on Monday, 2/20 due to Presidents Day.
 2/19: Solutions to Problem Set 3 have been posted.
 2/13: Solutions to Problem Set 2 have been posted.
 1/30: Solutions to Problem Set 1 have been posted.
 1/22: A sample MATLAB script to implement a switch has been posted.
 1/20: Datong's office hour on Wednesday, 1/25 is cancelled. Sorry, but I am out of town. Please send me an email.
 1/20: Datong's office hour on Monday, 1/23 has been shifted to 1:15  2:15 pm (Cory 212).
 1/19: Problem Set 1 has been posted (due 1/26).
 1/18: Datong's office hours start Monday, 1/23.
 1/16: The first lecture takes place tomorrow, 1/17 in 103 Moffitt.
Course Description
First graduate level course in nonlinear systems and control. Introduction to nonlinear
phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical
behavior. Planar dynamical systems, analysis using phase plane techniques.
Describing functions. Inputoutput analysis and stability. Lyapunov stability
theory. The Lure problem, Circle and Popov criterion. Feedback linearization,
sliding mode control. The course will be punctuated by a rich set of examples,
ranging from violin strings to jet engines, from heart beats to artificial
neurons, and from population growth to nonlinear flight control.

Introduction to Nonlinear Phenomena: Multiple Equilibria, Limit Cycles,
Complex Dynamics, Bifurcations

Second Order Nonlinear Systems: Phase Plane Techniques, Limit Cycles 
PoincareBendixson Theory, Index Theory

Inputoutput analysis and stability: Small Gain Theorem, Passivity, Describing
Functions

Lyapunov Stability Theory: Basic stability and instability theorems, LaSalle's
theorem, Indirect method of Lyapunov

Nonlinear Control: Linearization by State Feedback for SISO and MIMO systems,
Involutivity, Lie Brackets, Frobenius' Theorem,
Zero Dynamics, Inversion, Tracking, Stabilization
Handouts
 1/17: Course Outline (PDF)
 1/17: Lecture Notes 1 (PDF)
 1/23: Lecture Notes 2 (PDF)
 1/25: Lecture Notes 3 (PDF)
 1/30: Lecture Notes 4 (PDF)
 2/1: Lecture Notes 5 (PDF)
 2/6: Lecture Notes 6 (PDF)
 2/9: Lecture Notes 7 (PDF)
 2/16: Lecture Notes 8 (PDF)
 2/17: Lecture Notes 9 (PDF)
 2/23: Extra Lecture on Nyquist for Describing Functions (PDF)
 2/28: Lecture Notes 10 (PDF)
 2/28: Lecture Notes 11 (PDF)
 3/1: Lecture Notes 12 (PDF)
 3/2: Lecture Notes 13 (PDF)
 3/9: Lecture Notes 14 (PDF)
 3/22: Correction to Lecture Notes 14 (PDF)
 3/22: Lecture Notes 15 (PDF)
 4/3: Lecture Notes 16 (PDF)
 4/3: Lecture Notes 17 (PDF)
 4/10: Lecture Notes 18 (PDF)
 4/11: Lecture Notes 19 (PDF)
 4/11: Lecture Notes 20 (PDF)
 4/17: Lecture Notes 21 (PDF)
 4/17: Lecture Notes 22 (PDF)
 4/17: Lecture Notes 23 (PDF)
Homework
Old Exams
 3/9: Practice Midterm (S'15)
Discussion Sections
 2/3: Discussion 1 (PDF)
 2/10: Discussion 2 (PDF)
 2/17: Discussion 3 (PDF)
 2/24: Discussion 4 (PDF)
 3/3: Discussion 5 (PDF)
 3/10: Discussion 6 (PDF)
 3/24: Discussion 7 (PDF)
 4/7: Discussion 8 (PDF)
 4/14: Discussion 9 (PDF)
Links
Mailing List
Please sign the handout sheet on the first day of lectures (Tues Jan 17), OR
email Professor Tomlin, so that your email will be added to the class mailing
list.
Grading
Homework 30%
Midterm 30%
Final 40%
Notes and Textbook
The course is based on a set of lecture notes which will be made available
throughout the term.
The textbook for the course is:
S. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. SpringerVerlag,
1999. We will be covering topics from Chapters 1, 2, 5, 9, 10, and selected topics from
Chapters 3, 4, and 6.