Syllabus

The Ohio State University

Dept. Electrical and Computer Engineering

## ECE 6754: Nonlinear Systems Theory

**Instructor:** Prof. Passino, 416 Dreese Labs

**Office Hours:** By appointment (send an email to passino.1), and after class

**Textbook:** H. Khalil, Nonlinear Systems, 3^{rd} Ed., Prentice Hall, 2002

**Topics of Lectures:**

- Modeling, nonlinearities
- Phase plane, equilibrium types, periodic orbits
- Fundamental properties: Existence and uniqueness of solutions, comparison principle, etc
- Lyapunov stability, autonomous systems, instability
- LaSalle’s invariance principle
- Stability of nonautonomous systems
- Comparison functions
- Boundedness and uniform ultimate boundedness
- Input to state stability
- Small-gain theorem
- Passivity: Memoryless functions, state models, positive real transfer functions
- Passivity theorems
- Center manifold theorem, region of attraction, invariance-like theorems, stability of periodic solutions
- Stability of perturbed systems
- Perturbation theory and averaging
- Singular perturbations
- Feedback control

**Grading (tentative):**

- Homework: 60%
- Final exam: 40%

**Prerequisites:** Ordinary differential equations, linear systems, ECE 3551, ECE 5551