Nonlinear Systems Theory

Subject ELEN90028 (2015)

Note: This is an archived Handbook entry from 2015.

Credit Points: 12.5
Level: 9 (Graduate/Postgraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2015:

Semester 1, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period 02-Mar-2015 to 31-May-2015
Assessment Period End 26-Jun-2015
Last date to Self-Enrol 13-Mar-2015
Census Date 31-Mar-2015
Last date to Withdraw without fail 08-May-2015

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 36 hours of lectures
Total Time Commitment:

200 hours


Enrolment in a research higher degree (Masters or PhD) in Engineering



Recommended Background Knowledge:


Non Allowed Subjects:


Core Participation Requirements:

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements of this entry. The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website:


Marcus Nathan Brazil


Subject Overview:


The aim of this subject is to give students an introduction to some advanced topics in the analysis of nonlinear systems.


Topics include: properties of solutions of nonlinear differential equations; Lyapunov stability theory; linearization; the invariance principle; converse stability theorems; input-output stability; stability of perturbed systems; averaging, singular perturbations.

Learning Outcomes:


On completing this subject the student should be able to:

  1. Understand the fundamental properties of nonlinear systems, such as the existence, uniqueness and continuity of solutions
  2. Apply fundamental Lyapunov stability techniques in the analysis of nonlinear systems, as they arise in a variety of contexts
  3. Apply input-output stability concepts for stability analysis of interconnected nonlinear systems
  4. Apply averaging techniques for approximation of solutions and stability analysis of nonlinear systems
  5. Apply singular perturbation techniques for approximation of solutions and stability analysis of nonlinear systems.

  • Continuous assessment of homework assignments, not exceeding 30 pages in total over the semester (approximately 55-60 hours of work), worth 40%
  • Final examination at the end of semester, worth 60%.

Hurdle requirement: Students must pass the end of semester examination to pass the subject.

Intended Learning Outcomes (ILOs) are assessed in the final exam and the submitted assignments.

Prescribed Texts:


Recommended Texts:

Hassan Khalil, "Nonlinear Systems"

Breadth Options:

This subject is not available as a breadth subject.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
Generic Skills:
  • Ability to apply knowledge of basic science and engineering fundamentals
  • In-depth technical competence in at least one engineering discipline
  • Ability to undertake problem identification, formulation and solution
  • Ability to utilise a systems approach to design and operational performance
  • Expectation of the need to undertake lifelong learning, capacity to do so
  • Capacity for independent critical thought, rational inquiry and self-directed learning
  • Intellectual curiosity and creativity, including understanding of the philosophical and methodological bases of research activity
  • Openness to new ideas and unconventional critiques of received wisdom
  • Profound respect for truth and intellectual integrity, and for the ethics of scholarship.
Related Course(s): Master of Philosophy - Engineering
Ph.D.- Engineering

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