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Department of Mathematical Sciences, Unit Catalogue 2011/12

MA50046: Linear control theory

Click here for further information Credits: 6
Click here for further information Level: Masters UG & PG (FHEQ level 7)
Click here for further information Period: Semester 1
Click here for further information Assessment: CW 25%, EX 75%
Click here for further information Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Click here for further information Requisites:
Click here for further information Description: Aims & Learning Objectives:
The course is intended to provide an elementary and accessible introduction to the state-space theory of linear control systems. Main emphasis is on continuous-time autonomous systems, although discrete-time systems will receive some attention through sampling of continuous-time systems. Contact with classical (Laplace-transform based) control theory is made in the context of realization theory.
Objectives: To instill basic concepts and results from control theory in a rigorous manner making use of elementary linear algebra and linear ordinary differential equations. Conversance with controllability, observability, stabilizabilty and realization theory in a linear, finite-dimensional context. Students should be able to demonstrate an in-depth understanding of the subject.

Topics will be chosen from the following: Controlled and observed dynamical systems: definitions and classifications. Controllability and observability: Gramians, rank conditions, Hautus criteria, controllable and unobservable subspaces. Input-output maps. Transfer functions and state-space realizations. State feedback: stabilizability and pole placement. Observers and output feedback: detectability, asymptotic state estimation, stabilization by dynamic feedback. Discrete-time systems: z-transform, deadbeat control and observation. Sampling of continuous-time systems: controllability and observability under sampling.
Click here for further informationProgramme availability:

MA50046 is Optional on the following programmes:

Department of Mathematical Sciences
NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.