MSc Advanced Control and Systems Engineering / Course details

Brief description of the unit:

Part 1 - Linear Algebra

• Linear subspaces
• Eigenvalues and Eigenvectors
  Matrix inversion formulas
• Invariate subspaces
• Vector norms and matrix norms
• Singular value decomposition
• Generalised inverses
• Semidefinite matrices

Part 2 - Linear Dynamical Systems

• Description of linear dynamical systems
• Solutions of linear dynamical systems and their stability
• Controllability and observability
• Observers and observer-based controllers
• Operation on systems
• State-space realisations for transfer functions
• Hidden modes and pole-zero cancellation

Part 3 - Feedback System

• Feedback structure
• Well-posedness of feedback system
• Closed-loop stability

The unit aims to introduce the essential linear algebra concepts used in the development of the mathematical descriptions of linear system theory; to establish the mathematical foundations of linear dynamical systems used in control system theory; to give students a sound understanding of the state-space representation of linear dynamical systems and to formulate the stability of closed-loop systems.

ILO1 Analyse the preoerties of a matrix such as eigenvalues, norms, and singular values in the context of dynamical systems. [Developed and Assessed].

ILO2 Compute the invariate subspaces of a matrix and other significant properties. 

ILO3 Describe dynamical systems in mathematical terms using state-space representations. 

ILO4 Analyse dynamical system properties of state-space models. 

ILO5 Develop feedback controllers for state-space models using state-feedback and observer techniques.

ILO6 Analyse feedback dynamical systems and their properties.

Lectures, tutorials, practical/ laboratory work and private study.

Examination - four questions, answer all questions. Feedback is provided after the examination board. 

Laboratories - Quiz and Report. Feedback is provided two weeks after report submission.

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