Algebraic Construction of Normalized Coprime Factors for Delay Systems

Abstract.

We introduce an algebraic approach to the problem of constructing normalized coprime factorizations for retarded delay systems. A parametrization is given of all the possible factorizations that can be obtained by solving algebraic equations over the field generated by s and e ^−s. This enables us to provide a means of determining when such factors can be calculated by solving such algebraic equations, and to show that in general they cannot. Some illustrative examples are given.