Partington, J. R.; Sankaran, G. K. Algebraic construction of normalized coprime factors for delay systems. (English) Zbl 0998.93021 Math. Control Signals Syst. 15, No. 1, 1-12 (2002). An algebraic approach to the problem of constructing normalized coprime factorizations for retarded delay systems is given. The main result of this paper is a parametrization of all the possible factorizations that can be obtained by solving algebraic equations over the field generated by \(s\) and \(e^{-s}\). This parametrization result provides us with a means of determining when such factors can be calculated by solving such algebraic equations. In particular, it follows that in general this cannot be done. These results are then illustrated by a number of examples. Reviewer: Birgit Jacob (Dortmund) MSC: 93C23 Control/observation systems governed by functional-differential equations 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators Keywords:delay systems; normalized coprime factorization; spectral factorization; commutative algebra; Galois theory PDFBibTeX XMLCite \textit{J. R. Partington} and \textit{G. K. Sankaran}, Math. Control Signals Syst. 15, No. 1, 1--12 (2002; Zbl 0998.93021) Full Text: DOI