Exponential Characterization in Linear Viscoelasticity Under Delay Perturbations

摘要

We present a complete characterization of the (uniform) exponential stabilization for a class of viscoelastic models under small delay perturbations. The main ingredient under consideration is the notion of admissible kernels. While in the standard literature it is mostly common to request a exponential/general kernel as a sufficient condition for the exponential/general stability of the whole viscoelastic system under study, here our objective is to employ the much more general concept of admissible kernels and prove that it is not only sufficient but also a necessary assumption for exponential stability in linear viscoelasticity under small delay perturbations.