EECS 222

Nonlinear Systems: Analysis, Stability and Control

Shankar Sastry

299 Cory Hall
Tu-Th 11-12:30 pm.

We hear the term "this is so non-linear" or the term "these are really nonlinear effects" progressively more and more frequently now-a-days. While, this is often a statement used to mean "I give up" or "I simply don't know what is going on", more often than not, it is really an expression to suggest that the system in question is behaving in a complicated fashion.
This class is a modern introduction to the analysis, stability theory and control of nonlinear systems. The class starts with an introduction to the qualitative theory of nonlinear systems, with special attention being paid to the development of intuition on 2-D systems. This is followed by the development of the mathematical background necessary to study nonlinear systems.
We develop in detail the stability theory for nonlinear systems, so called Lyapunov theory with its application to many problems including stabilization, the Lur'e problem, adaptive control problems.
We finally develop the geometric theory of nonlinear control, including linearization by state feedback for SISO and MIMO systems, zero dynamics of nonlinear systems, decoupling by state feedback. We discuss observers for nonlinear systems and rudiments of constructive controllability and observability.
This is a busy and sophisticated course, but how much one gets out of the course is primarily a function of what one puts into the course both in terms of supplementary reading and contemplation. Enjoy!

Office Hours

Office: 284 HMMB

Office Hours: Monday Wednesday 3:00pm-4:00pm




Homework 30%
Midterm (1 Day Take Home) 30%
Final Exam (1 Day Take Home) 40%


Some introduction to linear systems theory and mathematical analysis is desirable. Thus, for example a course like EECS 221A and Math 104A is desirable. However, sophistication of thought is more important than formal pre-requisites


S. S. Sastry, "Nonlinear Systems: Analysis, Stability and Control," Springer Verlag, 1999.

Course Outline

2007 Course Outline, Additional References.

Homework Sets

Problem Set 1 , Issued January 18th, due February 1st, 2007. Typo on Line 1 of Problem 4, the invariant set should have radius sqrt lambda rather than 1. Solution Set will be posted on February 4th 2007.

Solutions to Problem Set 1

Problem Set 2 , Issued February 1st, 2007, due February 15th, 2007.

Solutions to Problem Set 2

Problem Set 3 , Issued February 15th, 2007, originally due March 1, 2007: now due March 8th.

Problem Set 4 , Issued March 6th, 2007, due March 22nd, 2007.

Matlab Tutorials and Links

Online Control Tutorial for Matlab
Matlab Documentation Help Desk
ODE software for Matlab for plotting phase portraits, by Professor John C. Polking, Rice University, TX.

Links to other related courses

Professor Claire Tomlin, University of California, Berkeley EECS 222, Nonlinear Systems: Analysis, Stability and Control Spring 2006. See especially the detailed lecture notes of Professor Tomlin scanned in.
Professor Claire Tomlin, Stanford University E209A: Analysis and Control of Nonlinear Systems Winter Quarter 2007
Professor Yi Ma, University of Illinois, Urbana Champaign ECE 528, Analysis of Nonlinear Systems Spring 2006