ELL 702: Nonlinear Systems

Nonlinear Systems course covers the analysis of nonlinear control systems. By the end of the course, it is expected that the students would have learned about various tools to analyze nonlinear systems and played around with a variety of interesting nonlinear examples. The analysis tools covered in this course would lay the foundation for designing controllers for nonlinear systems in ELL801.

Class Information

• Lecture schedule: Mondays and Thursdays, 2-3.20pm, LH614

• Teaching assistant: Soutrik Bandyopadhyay

• Office hours: Wednesdays, 3-4pm (Soutrik) and Fridays, 1-2pm (Priyank)

• Mid-term: September 12, 2024, 1-3pm, LH510

List of Topics (Tentative)

• Introduction
  

• Planar dynamical systems
  

• Existence and uniqueness of solutions
  

• Lyapunov stability
  

• Input-to-state stability
  

• Perturbation theory
  

• Averaging
  

• Singular perturbations
  

• Barrier functions
  

Homeworks

• Homework#1 (due August 12, 2024)

• Homework#2 (due August 22, 2024)

• Homework#3 (due September 2, 2024)

• Homework#4 (due September 9, 2024)

• Homework#5 (due September 19, 2024)

• Homework#6 (due October 3, 2024)

• Homework#7 (due October 24, 2024)

• Homework#8 (due November 7, 2024)

Prerequisties

• Basic knowledge of state space models, differential equations, and linear algebra
  

• Familiarity with any simulation software (Matlab, Mathematica, Python, etc.)

Grading Policy

• Homeworks: 60%
  

• Mid-term: 15%
  

• Major: 25%

References

• H. K. Khalil. Nonlinear Systems. Prentice Hall, 3rd edition, 2002

Useful Software

• pplane