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:
- Mathematical background.
- Fundamental properties of dynamical systems: existence and uniqueness of solutions, continuous dependence on initial conditions and parameters, comparison principles.
- Stability analysis: Lyapunov stability of autonomous and nonautonomous systems, LaSalle’s invariance principle, converse Lyapunov theorems, stability of feedback systems, effects of perturbations.
- Systems with inputs and outputs: input-to-state stability and related notions, Lyapunov characterizations.
- Nonlinear control: control Lyapunov functions, universal formulas for feedback stabilization and disturbance attenuation.
- 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.
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