University of California at Berkeley
Department of Electrical Engineering and Computer Sciences
Nonlinear Systems: Analysis, Stability, and Control
Spring Semester 2020
UCB On-Line Course Catalog and Schedule of Classes
Lecture Information: TuTh 2-3:30, 105 North Gate.
Discussion Information: Fridays 2:30-4, Cory 540
Professor Claire J. Tomlin,
721 SD Hall
tomlin at eecs.berkeley.edu
Office hours: Tu 11-12, Wed 11-12
337 Cory Hall
westenbroekt at berkeley.edu
Office hours: Mon 10-11, Thur 10-11 in Cory 337
- 1/16: The first lecture takes place on 1/21 in 105 North Gate.
- 1/23: There will be a discussion on Friday 1/24, 2:30-4 in Cory 540
- 2/7: The midterm will take place on Thursday March 5, in class
- 2/17: Starting with homework 4, we will now accept late submissions for homework on gradescope with 10% taken off each 24 hours after the submission.
- 3/4: As announced to the class email list today, the midterm test tomorrow will be a "take-home" test.
The test will be provided to you online at 2:10pm tomorrow, and we require that you
return it to us using bCourses, by 4pm tomorrow. This is meant to be a 1 hour and 20 minute
test, and the extra time allows you to find a quiet place to work if you
are coming from another class, download the test, and scan your solutions back for upload.
We will send another email with instructions on downloading the test.
The Honor Code is in effect: don't talk with others while taking the test,
and use only your prepared crib sheet as supplemental material.
- 4/28: The final will be a take home exam, and you will have 24 hours to complete the exam.
You are free to use your notes, textbooks, and lecture notes during the exam.
The exam will be emailed to you at one of the following times, and you must upload it to Gradescope 24 hours after it was emailed to you. You may choose one of the following times (US Pacific time) to start the exam:
Group 1: Thursday May 7 9am;
Group 2: Thursday May 7 9pm;
Group 3: Monday May 11 9am;
Group 4: Monday May 11 9pm.
Please let us know by May 6 at 5pm which group you prefer,
by entering your name and preferred email to use for the exam, on the
If you do not enter your name, we will assume that you choose Group 4.
The Honor Code is in effect: don't talk with others while taking the test, and do not pass information about the test to anyone until the entire exam period is over.
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. Input-output analysis and stability. Lyapunov stability
theory. The Lure problem, Circle and Popov criterion. Control Lyapunov Functions.
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 -
Poincare-Bendixson Theory, Index Theory
Input-output analysis and stability: Small Gain Theorem, Passivity, Describing
Lyapunov Stability Theory: Basic stability and instability theorems, LaSalle's
theorem, Indirect method of Lyapunov, Control Lyapunov Functions
Nonlinear Control: Linearization by State Feedback for SISO and MIMO systems,
Involutivity, Lie Brackets, Frobenius' Theorem,
Zero Dynamics, Inversion, Tracking, Stabilization
- 1/16: Course Outline (PDF)
- 1/16: Lecture Notes 1 (PDF)
- 1/16: Lecture Notes 2 (PDF)
- 1/28: Lecture Notes 3 (PDF)
- 1/30: Lecture Notes 4 (PDF)
- 1/30: Lecture Notes 5 (PDF)
- 2/6: Lecture Notes 6 (PDF)
- 2/6: Lecture Notes 7 (PDF)
- 2/11: Lecture Notes 8 (PDF)
- 2/11: Lecture Notes 9 (PDF)
- 2/13: Lecture Notes 10 (PDF)
- 2/13: Lecture Notes 11 (PDF)
- 2/13: Lecture Notes 12 (PDF)
- 2/24: Lecture Notes 13 (PDF)
- 2/26: Lecture Notes 14 (PDF)
- 3/5: Correction to Lecture Notes 14 (PDF)
- 3/5: Lecture Notes 15 (PDF)
- 3/5: Lecture Notes 16 (PDF)
- 3/5: Lecture Notes 17 (PDF)
- 4/6: Special Lecture on Control Lyapunov Functions (PDF).
These are course notes from Professor Koushil Sreenath's 237/222 lectures last Fall, transcribed by Chih-Yuan (Frank)
Chiu. The lectures notes were inspired by similar lecture by Professor Jessy Grizzle (U. Michigan).
- 4/6: Lecture Notes 18 (PDF)
- 4/9: Lecture Notes 19 (PDF)
- 4/9: Lecture Notes 20 (PDF)
- 4/23: Lecture Notes 21 (PDF)
- 4/23: Lecture Notes 22 (PDF)
- 4/23: Lecture Notes 23 (PDF)
Recorded Lectures (week of 3/9 used Course Capture; starting 3/16 recorded directly)
Please sign the handout sheet on the first day of lectures (Tues Jan 21), OR
email Professor Tomlin, so that your email will be added to the class mailing
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. Springer-Verlag,
1999. We will be covering topics from Chapters 1, 2, 5, 9, 10, and selected topics from
Chapters 3, 4, and 6.