EE613: Nonlinear Dynamical Systems (Autumn 2020)

ANNOUNCEMENTS: Welcome. Please familiarize yourselves with Google Classroom

Instructor: Dr. Debraj Chakraborty

Email: dc [AT] ee.iitb.ac.in

Office: New Office Complex, 1^st floor, EE

Lecture Hours: Slot 2 (Google Classroom Code: 33lzvmb)

Website: http://www.ee.iitb.ac.in/~dc/EE613

TAs: TBA

• Prereq: Familiarity with Linear Systems and Linear Algebra( e.g. EE640 or (EE302 + EE635) )

Syllabus

1. Analysis:

a. Phase Plane Analysis: Linear and Nonlinear Systems, Periodic Solutions and Limit Cycles.

b. Existence and Uniqueness of Solutions of Nonlinear Differential Equations

c. Lyapunov Stability: Direct and Indirect Methods.

d. Stability of Non-Autonomous Systems: Lyapunov Methods, Input Output Stability: Small-Gain Theorem

e. Frequency Domain Analysis: Passivity and Positive Linear Systems, Lure Problem, Circle and Popov Criterion

2. Synthesis: Feedback Linearization, Sliding Mode Control, (If time permits) Lyapunov Redesign, Backstepping, Passivity Based Control

Text Book

No Text Book is prescribed. Lecture Notes will be provided.

Reference Books

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

2. J. J. Slotine and W. Li, Applied Nonlinear Control, Prentice- Hall, 1991.

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

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

Evaluation:

Assignments (20%), Mid-Sem (30%), End-Sem (40%), Term Project (10%) .

Lecture Notes

1. Lecture 1 : Introduction

2. Lecture 2: Second Order Systems

3. Lecture 3: Uniqueness and Existence

4. Lecture 4: Lyapunov Theory

5. Lecture 5: Input-Output Stability

6. Lecture 6: Passivity

7. Lecture 7: Lure Problem and Circle Criterion

8. Lecture 8: Controller Design Techniques

Homework Assignments

1. Four Homework assignments - TBA

Term Project:

Term project - a) Abstract submission deadline:- TBA
b) Final report submission deadline:- TBA