论文标题
padé近似和超几何函数：与延迟分化方程频谱的缺失链接
Padé Approximation and Hypergeometric Functions: A Missing Link with the Spectrum of Delay-Differential Equations
论文作者
论文摘要
众所周知，有理近似理论涉及退化的高几何函数，尤其是指数函数的padé近似与Kummer高几何函数密切相关。最近，在研究延迟差异方程的琐碎解的指数稳定性的背景下，强调了退化的超几何函数与与线性延迟分差方程相关的特征函数的零之间的新链接。这样的链接允许表征被称为多重性引起的占主导地位（中）的时间延迟系统的属性，该系统通过使用部分极点放置想法为时间延迟系统设计了一个新的方向。由于它们与高几幅功能的关系，我们在本文中探索了延迟分化方程和指数函数的padé近似之间的联系。本说明利用并进一步评论了[I。 Boussaada，G。Mazanti和S-I。 niculescu。 2022年，Comptes Rendus。 Mathématique，Arxiv：2107.11363]和[I. Boussaada，G。Mazanti和S-I。 niculescu。 2022年，SciencesMathématiques，Arxiv：2106.03378]。
It is well known that rational approximation theory involves degenerate hypergeometric functions and, in particular, the Padé approximation of the exponential function is closely related to Kummer hypergeometric functions. Recently, in the context of the study of the exponential stability of the trivial solution of delay-differential equations, a new link between the degenerate hypergeometric function and the zeros distribution of the characteristic function associated with linear delay-differential equations was emphasized. Such a link allowed the characterization of a property of time-delay systems known as multiplicity-induced-dominancy (MID), which opened a new direction in designing low-complexity controllers for time-delay systems by using a partial pole placement idea. Thanks to their relations to hypergeometric functions, we explore in this paper links between the spectrum of delay-differential equations and Padé approximations of the exponential function. This note exploits and further comments recent results from [I. Boussaada, G. Mazanti and S-I. Niculescu. 2022, Comptes Rendus. Mathématique, arXiv:2107.11363] and [I. Boussaada, G. Mazanti and S-I. Niculescu. 2022, Bulletin des Sciences Mathématiques, arXiv:2106.03378].
