Nonlinear Systems Theory (ELEN90028)
Graduate courseworkPoints: 12.5Not available in 2025
About this subject
Overview
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AIMS
The aim of this subject is to give students an introduction to some advanced topics in the analysis of nonlinear systems.
INDICATIVE CONTENT
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.
Intended learning outcomes
INTENDED LEARNING OUTCOMES (ILOs)
On completing this subject the student should be able to:
- Understand the fundamental properties of nonlinear systems, such as the existence, uniqueness and continuity of solutions
- Apply fundamental Lyapunov stability techniques in the analysis of nonlinear systems, as they arise in a variety of contexts
- Apply input-output stability concepts for stability analysis of interconnected nonlinear systems
- Apply averaging techniques for approximation of solutions and stability analysis of nonlinear systems
- Apply singular perturbation techniques for approximation of solutions and stability analysis of nonlinear systems.
Generic skills
On completion of this subject, students will have developed the following 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.
Last updated: 4 March 2025
Eligibility and requirements
Prerequisites
Admission into a research higher degree (MPhil or PhD) in Engineering.
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 4 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Continuous assessment of homework assignments, not exceeding 30 pages in total over the semester (Addressing ILOs 1-5)
| Throughout the semester | 40% |
Final examination (Addressing ILOs 1-5) Hurdle requirement: Students must pass the end of semester examination to pass the subject. | End of semester | 60% |
Last updated: 4 March 2025
Dates & times
Not available in 2025
Time commitment details
200 hours
Last updated: 4 March 2025
Further information
- Texts
- Related Handbook entries
This subject contributes to the following:
Type Name Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Additional information for this subject
Subject coordinator approval required
- Available to Study Abroad and/or Study Exchange Students
Last updated: 4 March 2025