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TW 286
W.Michiels, K.Engelborghs, and D.Roose
Sensitivity to infinitesimal delays in neutral equations
Abstract
In this paper we investigate the sensitivity of the stability of neutral functional differential equations with respect to changes in the delays. This sensitivity is caused by the behaviour of the essential spectrum which in turn, is determined by the roots of an exponential polynomial. In [1], Avellar and Hale considered the case of multiple fixed and nonzero delays. In a first part we visualize and interpret their results by means of computational spectral plots. In a second paert we extend the theory of [1] to the important limit case of arbitrary small delays and show that this can lead to eigenvalues with arbitrary large positive real part. Necessary and sufficient conditions are provided. We conclude with two illustrative examples. The first of these is the analysis of the robustness of a boundary controlled partial differential equation in the presence of small feedback delays.
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