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
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