Stabilization of abstract delay systems on banach lattices using nonnegative semigroups

In this study, we investigate the problem of designing a linear state feedback control to stabilize a class of linear uncertain systems with state delay. We introduce the concept of an abstract delay system that can be used to characterize the behavior of a broad class of mathematical models that include 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 nonnegative semigroup on a Banach lattice. The objective of this paper is to show that the stabilizability conditions obtained by a stability criterion of nonnegative semigroups have a particular geometric configuration with respect to the permissible locations of uncertain entries. For this purpose, we introduce a variable transformation method to eliminate a restrictive assumption such as the nonnegativity of a system.