Abstract

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.

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