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Nonlinear Systems Theory (ELEN90028)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Year of offer2019
Subject levelGraduate coursework
Subject codeELEN90028
Semester 1
FeesSubject EFTSL, Level, Discipline & Census Date


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.

Intended 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.

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: 22 August 2019