Aims & Learning Objectives: Aims: The course is intended to provide an elementary and assessible 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.
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.
