Polynomial decay rate estimates in Banach spaces for bilinear neutral systems with distributed delay

Abstract

The present paper focuses on the feedback stabilization of infinite dimensional bilinear neutral systems with distributed delay, evolving on a Banach state space. Under an appropriate state space decomposition, we consider a feedback control based only on the projected state onto a relevant subspace and analyze its ability to achieve strong and polynomial stabilization. An explicit decay estimate of the stabilized solution is derived. The effectiveness of the theoretical results is further demonstrated through examples and numerical simulations.