Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstractsecond-order infinite-dimensional dynamical systems is considered.Using the frequency-domain method, it is proved that approximatecontrollability of such a system follows from that of a suitablydefined first-order system. The general results are then appliedto investigating the approximate controllability of a vibratorydynamical system modelling a flexible mechanical structure.Some special case are also considered. Moreover, remarks andcomments on the relationships between different concepts ofcontrollability are given. The paper generalizes earlier resultson second-order abstract dynamical systems.