EE613 – Non-linear Dynamical Systems

Course Offered in: (2011-2012)

Course Contents:

Formal Syllabus + text books can be found here.

Course Contents:

Linear Systems: Stability, Speed
Analysis by phase plane and describing function methods.
Lyapunov stability theory
Popov’s method, circle criterion
Lagrangian and gradient systems: physical examples and analysis.
Stability of Hamiltonian systems.
Periodic systems

Prerequisites:

MA 108(Differential Equations) and EE 302(Control Systems). This is a very logical course and all math lovers will surely like it. However, it is related to the study of stability of various linear/nonlinear input-output systems, and a very strong understanding of control systems is required; especially in the latter half of the course.

Future Courses based on this course:

This course will basically equip you with tools to analyse the stability of systems; so it’s useful everywhere. For example, I used concepts from this course in my course project in ‘Wavelets’.

Textbook:

Hassan Khalil, Nonlinear Systems, 2nd Edition,Prentice Hall
M. Vidyasagar, Nonlinear systems analysis. 2nd Edition. Prentice Hall, 1993.

Refer to Khalil- it is a very good book.

Software:

None

Professor’s who have taken it in the past:

Prof. Harish Pillai, Prof. Madhu Belur. This year, it is Prof V.R.Sule who will be taking it.

Miscellaneous:

This course is slightly abstract, but fairly logical. You’ll be analysing the stability of different linear/nonlinear systems using a variety of tools in this course. It’s extremely interesting and has a lot of applications in other courses as well. A good understanding of control systems is required, since this course won’t cover those concepts again, but will build upon them. There is a fair amount of mathematical rigor required in this course, so refrain from taking it up if you aren’t too fond of maths (or control systems).

Review by: Gouri Nawathe. You can contact her on gouri.nawathe@gmail.com for further queries.