Well-Posedness and admissible stabilizability for Pritchard-Salamon systems

In this note, we obtain a perfect characterization of generator of the perturbation semigroup for Pritchard-Salamon systems. From this we give a much simpler and more straight proof of the theorem on nest of feedback loop and answer the open problem posed by Curtain, Logemann, Townley and Zwart. More precisely, we establish that the smooth condition is unnecessary in the constructive argument for Pritchard-Salmon systems.