Controllability in continuous-time systems with digital controllers

The purpose of this paper is the study of controllability properties of a continuous-time system controlled by a digital controller. The study is carried out in the modern lifting framework in which the continuous-time periodicity of such an overall system, called also a sampled-data system, is converted into time-invariance of an infinite-dimensional input/output system in discrete-time. Different concepts of controllability related directly to the continuous-time behavior of sampled-data systems axe introduced, namely exact, approximate and null controllability. It is shown that the two former notions never occur in sampled-data systems while the latter notion is a generic property for these systems