Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstract second-order infinite-dimensional dynamical systems is considered. Using the frequency-domain method, it is proved that approximate controllability of such a system follows from that of a suitably defined first-order system. The general results are then applied to investigating the approximate controllability of a vibratory dynamical system modelling a flexible mechanical structure. Some special cases are also considered. Moreover, remarks and comments on the relationships between different concepts of controllability are given. The paper generalizes earlier results on second-order abstract dynamical systems.