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