Finite rank stabilizability and preservation of stabilizability under sampling for distributed parameter systems

Considered are the notion of stabilizability (and the dual notion of detectability) for infinite dimensional systems and some questions that arise in its relation to, and interaction with, time sampling. More specifically, two questions are addressed involving the optimal linear quadratic (LQ) control of discrete-time infinite dimensional or distributed parameter systems. These are spectral decomposition and finite rank stabilizability of a continuous linear control system and stabilizability under sampling for infinite dimensional systems.<>