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Linear Systems Theory (ELEN90027)
Graduate courseworkPoints: 12.5Not available in 2024
Overview
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AIMS
This subject provides a rigorous introduction to the mathematical tools that underpin the analysis and design of dynamical systems, with a focus on the linear time-invariant case. The subject is intended for research higher-degree students in Engineering.
INDICATIVE CONTENT
Topics include:
- Linear Analysis – scalars, real-valued sequences, vector spaces, linear operators, matrix analysis in finite-dimensions, normed spaces, vector sequences, inner-product spaces, orthogonality, Banach and Hilbert spaces, invertibility, and spectral analysis;
- Sate-space models – linear differential equations, input-output maps, reachability, observability, Hankel operators, model reduction by balanced truncation;
- Feedback interconnections – transfer functions, internal stability, coprime factorization, a parametrization of all stabilizing controllers;
- Optimal filtering and control – quadratic measures of performance (H2 and H-infinity), spectral factorization, Riccati equations.
Intended learning outcomes
INTENDED LEARNING OUTCOMES (ILOs)
Upon completion of this subject, it is expected that the student will be able to:
- Apply the mathematics of linear analysis;
- Employ input-output and state-space methods in the study of linear dynamical systems and feedback interconnections of such systems;
- Formulate and solve optimal filtering and control problems.
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;
- Profound respect for truth and intellectual integrity, and for the ethics of scholarship.
Last updated: 30 January 2024
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: 30 January 2024
Assessment
Description | Timing | Percentage |
---|---|---|
Three homework assignments of equal weight, not exceeding a total of 45 pages of work
| From Week 4 to Week 12 | 60% |
One written "take-home" exam of a duration not exceeding eight hours
| During the examination period | 40% |
Additional details
Intended Learning Outcomes (ILOs) 1 to 3 are assessed in the final exam and through submitted homework assignments.
Last updated: 30 January 2024
Dates & times
Not available in 2024
Time commitment details
200 hours
Last updated: 30 January 2024
Further information
- Texts
Prescribed texts
None
- Subject notes
LEARNING AND TEACHING METHODS
This subject is delivered through lectures and homework assignments.
INDICATIVE KEY LEARNING RESOURCES
Students are provided with lecture notes, including worked examples, assignment problems, and recommended reading lists comprising textbooks and journal articles.
CAREERS / INDUSTRY LINKS
Exposure to research literature and the rigour expected at the level of postgraduate study.
- Related Handbook entries
This subject contributes to the following:
Type Name Course Doctor of Philosophy - Engineering Course Ph.D.- 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.
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
Last updated: 30 January 2024