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Linear Systems Theory (ELEN90027)

Graduate courseworkPoints: 12.5Not available in 2025

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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: 6 November 2025