MA50046: Linear control theory
[Page last updated: 15 October 2020]
Academic Year:  2020/1 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  
Description:  Aims & Learning Objectives: Aims: The course is intended to provide an elementary and accessible introduction to the statespace theory of linear control systems. Main emphasis is on continuoustime autonomous systems, although discretetime systems will receive some attention through sampling of continuoustime systems. Contact with classical (Laplacetransform 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, finitedimensional context. Students should be able to demonstrate an indepth understanding of the subject. Content: 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. Inputoutput maps. Transfer functions and statespace realizations. State feedback: stabilizability and pole placement. Observers and output feedback: detectability, asymptotic state estimation, stabilization by dynamic feedback. Discretetime systems: ztransform, deadbeat control and observation. Sampling of continuoustime systems: controllability and observability under sampling. 
Programme availability: 
MA50046 is Optional on the following programmes:Department of Mathematical Sciences

Notes:
