Controllability, observability and stabilizability of retarded systems

Several concepts of function space controllability and observability of linear retarded systems are re-examined from the point of view of abstract infinite-dimensional systems with state space Rn??L2. It is shown that the controllability of all the eigenmodes, hence feedback stabilizability with an arbitrary exponential decay rate, is implied by a property weaker than the approximate controllability in Rn??L2. Verifiable criteria for this type of controllability and for a related concept of observability are given, along with several examples.