A constructive algebraic analysis approach to Artstein's reduction of linear time-delay systems

Artstein's results show that a first-order linear differential system with delayed inputs is equivalent to a first-order linear differential system without delay under an invertible transformation which includes integral and time-delay operators. Within a constructive algebraic approach, we show how this reduction can be found again, generalized and interpreted as a particular isomorphism between modules defining the two above linear systems. Moreover, we prove that Artstein's reduction can be obtained in an automatic way by means of symbolic computation techniques, and thus can be implemented in dedicated computer algebra systems.