Rating the significance of infinite chains of poles in time delay systems

The asymptotic chains as typical feature of spectrum of retarded time-delay system are investigated by means of distribution diagram and on the basis of decomposing the system response into a residue-based partial fraction expansion. A novel method of rating the significance of the infinite chains of poles is presented based on evaluating the residues of the principal terms of the system transfer function. A truncation error estimate after neglecting an influence of the high frequency infinite chain to the weighting function is proposed based on partial fraction expansion.