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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

To select unit EEEN40221 you must have taken EEEN30231 Control Systems II in your 3rd year.

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.
Assessment Methods

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.

“Robust and Optimal Control” by Zhou, Doyle, and Glover.

“Linear Systems Theory” by Joao P. Hespanha

“Feedback control of dynamic systems” by Franklin and Powell, Prentice-Hall.

“Modern control systems” by Dorf and Bishop, Prentice-Hall.