Insights on Asymptotic Behavior of Characteristic Roots of Quasi-Polynomials with Delay-Dependent Coefficients in Some Ill-Posed Cases

This work focus on the asymptotic behavior of critical roots of linear time-delay systems with delay-dependent coefficients. Our main goal is to derive a simple methodology to characterize some ill-posed cases from the open literature. In order to accomplish such a task, our main tool will be to express the solutions as a convergent power series. More specifically, by means of an appropriate change of variable, the expansion of unbounded solutions is obtained, which allows to derive an appropriate auxiliary solution that serves to analyze the behavior of such solutions. One of the main benefits in adopting such an approach, is that stability analysis in the ill-posed cases can also be covered. © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

Delay-dependent Coefficients; Time-Delay Systems; Well-Posed Linear Systems Delay control systems; Linear systems; Time delay; Asymptotic behaviors; Change of variables; Characteristic roots; Delay dependent; Linear time-delay system; Stability analysis; Time-delay systems; Well posed linear system; Asymptotic analysis

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