Department of Mathematical Sciences, Unit Catalogue 2011/12
|Level:||Honours (FHEQ level 6)|
|Supplementary Assessment:||MA30046 Mandatory Extra Work (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must take MA20216 and take MA20218 and take MA20219 and take MA20220|
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.
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.
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.
MA30046 is Optional on the following programmes:Department of Mathematical Sciences