ELEC9732 - Analysis and Design of Non-linear Control

Last modified by Leon Luo on 2023/01/06 13:55


This subject, defined by it's course name, covers non-linear control theory. It is highly recommended that ELEC4631 and ELEC4632 should be taken before this course, ELEC9732, despite the lack of requisite courses in the handbook. These two courses, or equivalent assumed knowledge, are applied in this course. Furthermore, it is also highly recommended that students taking this course should have a strong mathematical background and the ability to manipulate mathematical expressions.


These concepts are studied through course content, mainly lecture notes and course recommended textbooks. Please note, unless referenced from another source, please assume the following information presented is interpreted, studied, and re-expressed from the course content. Furthermore, please refer to the course content directly, e.g. ask the lecturer or read the textbook, for the most relevant knowledge required for the course.

Non-linear Ordinary Differential Equations

Phase Plane Methods


Lyapunov Stability

If you have taken without 4631/4632 , Lyapunov stability theory and KL theorem can be quite helpful. Also there is no standard way to find lyapunov function and it is found by a guessing/observing. 

You cannot construct transfer functions to non linear systems so it had various methods to study the stability. One method is linearizing about a equilibrium point and finally studying eigen values to determine the stability like in linear control systems.
One method i found easy to prove EIEO systems is proving by Passivity way. Lyapunov functions generalize this notion of an energy function to more general systems[1]. Correct this if i am wrong but i am writing through my memory. Basically use lyapunov function and prove that it is less that product/function of uy.Thats it done and then add in some comments about EIEO.

Input/Output Stability

Non-linear Control

Feedback Linearisation

State Feedback Linearisation

Gain Scheduling

Sliding Mode Control

Backstepping Design Method

Recommended Resources

Course Prescribed


  • JJ Slotine, W Li (1991). Applied Nonlinear Control (Prentice Hall)
  • H Khalil (1996,2002) Nonlinear Systems (Prentice Hall)
  • S Sastry (1999) Nonlinear Systems (Springer).
  • A Isidori (1995) Nonlinear Control (Springer).


[1] http://underactuated.mit.edu/lyapunov.html


Tags: Control
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