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

  • Major: November 18, 2024, 1-3pm, LH316

List of Topics

  • Introduction

  • Planar dynamical systems

  • Existence and uniqueness of solutions

  • Lyapunov stability

  • Input-to-state stability

  • Stability of perturbed systems

  • Averaging

  • Singular perturbations

  • Input-output stability

  • Passivity

  • Finite-time stability

  • Stability of sets and Semistability

Homeworks

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

  • W. M. Haddad and V. Chellaboina. Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton University Press, 2008

  • S. S. Sastry. Nonlinear Systems: Analysis, Stability and Control. Number 10 in Interdisciplinary Applied Mathematics. Springer, 1999

  • M. Vidyasagar. Nonlinear Systems Analysis. Prentice Hall, 1978

Useful Software