Abstract
The paper describes a method of approximating a linear constant dynamic system having one state delay and modelled by a differential-difference equation, by an equivalent ordinary differential equation-system via decomposition of its spectrum. Using spectral theory of an unbounded operator, such an infinite dimensional system is projected into an abstract function space which is then decomposed into two closed sub-spaces, one of which is finite dimensional and spanned by the “dominant” eigenfunctions of the system, which are to be retained. This set, and a minimal one, is chosen by a criterion where responses of consecutive modes are compared. In this finite-vector space, the delay differential system is projected and adequately approximated, to any desired degree of accuracy, as an ordinary differential system whose dimension is larger than order of the delay system.
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