Linear control theory MAT3502

Course content:
Linear homogeneous systems of differential and difference equations.
Stability and asymptotic stability of continuous-time and discrete-time linear systems.
Different representations of control systems.
Controllability. Criteria of controllability.
Observability. Criteria of observability.
Realization problem for continuous-time and discrete-time linear systems. Different variants of the problem.
Realization of input-output operator.
Realization of transfer matrix and of higher order equation.
Minimal realizations. Uniqueness. Isomorphic realizations.
Feedback. Stabilization and stabilizability of continuous-time and discrete-time linear systems.
Relations between controllability and stabilizability.
Detectability and observers.
Canonical forms and transformations of control systems.
Optimal control problems.
Systems on time scales.

Learning outcomes: ability to analyse and construct linear control systems.