A Variable Transformation Method for Stabilizing Abstract Delay Systems on Banach Lattices

In this study, we introduce the concept of an abstract delay system that can be used to characterize the behavior of a wide class of mathematical models that include partial differential equations and delay differential equations. We examine the stabilization problem of an abstract delay system on a Banach lattice using semigroup theory. To tackle this problem, we take advantage of the properties of a non-negative $C_0$ semigroup on a Banach lattice. The objective of this paper is to propose a stabilization method for an abstract delay system on a Banach lattice. We derive a sufficient condition under which an abstract delay system is uniformly exponentially stabilizable. Furthermore, we provide illustrative examples to verify the effectiveness of the proposed method.