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Algebraic construction of normalized coprime factors for delay systems. (English) Zbl 0998.93021

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.

MSC:

93C23 Control/observation systems governed by functional-differential equations
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
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