ELL 702: Nonlinear Systems

Venue: IV-339, Time: MW 11-11:50am, Th 12-12:50pm

Syllabus

• Introduction to Non-linear Systems. Lecture 1

• Phase Portraits/Vector Fields and Equilibrium Points. Lecture 2 and Lecture 3

• Periodic Solutions. Lecture 4 and Lectures 5 and 6.

• Existence and Uniqueness of Solutions. Lectures 7 and 8 and Lectures 9, 10, and 11.

• Stability and Lyapunov's Theorems. Lectures 12 and 13, Lectures 14 and 15

• Input-output stability and small gain theorem. Lectures 16 and 17

• Dissipativity theory and Lur‘e problem. Lecture 18, Lecture 19, Lecture 20

• Describing Functions. Lecture 21

• Input-output feedback and state feedback linearization. Lecture 22 and Lecture 23

Reference Books

We will mainly follow the treatment given in following books-

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

• Hassan Khalil, Nonlinear Systems, 3rd Edition, Prentice-Hall, 2002.

• M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall, 1993.

• M. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, 1974.