An Integro-differential-delay Operator Approach to Transformations of Linear Differential Time-delay Systems

In this paper, we further develop the study of rings integro-differential-delay operators considered as noncommutative polynomial algebras satisfying standard calculus identities. Within algebraic analysis approach, show that transformations and reductions linear differential time-delay systems can be interpreted homomorphisms isomorphisms finitely presented left modules over an algebra operators. particular, how Fiagbedzi-Pearson's transformation found again generalized. This maps solutions a first-order system with state input delays to purely state-space system. reduces well-known Artstein's reduction when has no delay yields isomorphism solution spaces.