Geometric Linear Control Theory;

fundamental concepts related to (finite dimensional) linear time-invariant control system such as controllability, observability and stabilizability. These basic concepts will be introduced via the "geometric approach" meaning that they will be related to various subspaces related to the matrices appearing in the system equations. This approach will enable us to introduce the important notion of (A,B)-invariant subspace (and its dual concept, (C,A)-invariant subspace), which will be used to solve the disturbance decoupling problem (and can be used to solve the problem of tracking and regulation).
Moreover, the notion of (A,B)-invariant subspace and (C,A)-invariant subspace also turn out to be instrumental in other synthesis problems like observer design, system invertibility, the minimum phase property, and output stabilizability.