Generalized sampled data feedback control of distributed parameter systems

In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems the necessary conditions are also known to be sufficient. We show that this equivalence extends to the infinite-dimensional case if the underlying semigroup is analytic. However, for general systems, the necessary conditions are not sufficient, nor are the sufficient conditions necessary. We prove this by a single example with a free parameter – one choice of parameter shows that the necessary conditions are too weak, and another choice shows that the sufficient conditions are too strong.