My writeup of the solutions to homework 1 may be found here.

Homework 2 may be downloaded here. It will be due on March 13, 2004.

A brief write-up of the latter half of Tuesday’s lecture can be found here.

A nice exposition of existence and uniqueness for differential equations, roughly paralleling what we have covered, can be found in this set of lecture notes.

See here for lecture notes for the material we have covered in class from a previous semester of this class. Note that these notes are from a different instructor and so correspond only roughly to the our class sessions.

The first homework may be downloaded here. It will be due on Tuesday, Feb 18th.

Edit: The homework date above has been updated.

This is the website of ECE 528/GE520/ME 546, Analysis of Nonlinear Systems.

Course material, such as homeworks, relevant links, and occasional lecture notes will be posted here.

We will cover the following material:

1. Mathematical background.
2. Fundamental properties of dynamical systems: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, comparison principles.
3. Stability analysis: Lyapunov stability of autonomous and nonautonomous systems, LaSalle’s invariance principle, converse Lyapunov theorems, stability of feedback systems, effects of perturbations.
4. Systems with inputs and outputs: input-to-state stability and related notions, Lyapunov characterizations.
5. Nonlinear control: control Lyapunov functions, universal formulas for feedback stabilization and disturbance attenuation.
6. Advanced topics (time permitting): center manifold theorem, averaging, singular perturbations.

The syllabus may be downloaded here.

Some useful links:

• Lecture notes for a similar course at Berkeley.
• Lecture notes for a similar course at MIT.