Uniform Synchronization of an Abstract Linear Second Order Evolution System

Although mathematical study on the synchronization of wave equations at finite horizon has been well developed, there have few results for long-time horizon. The aim paper is to investigate uniform infinite one abstract linear second order evolution system in a Hilbert space. First, using classical compact perturbation theory stability semigroups contractions, we will establish lower bound number damping, necessary considered system. Then, under minimum clarify algebraic structure as necessity conditions compatibility coupling matrices. We then by method and give dynamics asymptotic orbit. Various applications are given with boundary feedback or (and) locally distributed feedback, Kirchhoff plate feedback. Some open questions raised end future development. based semigroups.