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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
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.
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: 3 November 2022