题目：Padé approximants, Kummer functions, and the spectrum of time-delay systems

报告人：Guilherme Mazanti, 法国国家信息与自动化研究所（Institut national de recherche en informatique et en automatique）

时间：4月8日（星期三）, 16:00-17:00

地点：东区第五教学楼5107教室

摘要：The aim of this talk is to highlight some old and more recent links between Padé approximants, Kummer functions, and the spectrum of time-delay systems. A Padé approximant of a function f, named after the french mathematician Henri Padé (1863–1953), is an approximation of f by a rational function, i.e., a fraction of two polynomials. These kinds of approximations have been used since at least the 18th century and find many applications, in particular in control engineering, where they are used to approximate time delays by ODEs. Indeed, the presence of a delay in a system yields an exponential term in its characteristic function, and a standard technique in control engineering is to approximate such an exponential term by a rational function. Padé approximants of the exponential function have been deeply studied and were the subject of Henri Padé's PhD thesis. In particular, the corresponding approximation error can be expressed in terms of a class of special functions, known as Kummer confluent hypergeometric functions. It turns out that these functions also appear in the expression of the characteristic function of a very particular class of time-delay systems, namely scalar systems with a single delay and whose characteristic function has a root of maximal multiplicity. Exploiting this connection, one can prove the so-called multiplicity-induced dominance property for this class of time-delay systems. This talk will explore all these connections between Padé approximants, Kummer functions, and the spectrum of time-delay systems.