时滞系统重根附近Puiseux级数计算中的矛盾现象

CONTRADICTIONS IN CALCULATING THE PUISEUX SERIES EXPANSION OF TIME-DELAY SYSTEMS NEAR A REPEATED CHARACTERISTIC ROOT

Puiseux级数是研究时滞系统在重特征根附近动力学的一种数学工具,近年来已成为国内外一个研究热点.本文发现,在某些情况下,利用待定系数法求时滞系统的Puiseux级数时会出现矛盾现象,进而给出了产生矛盾的原因和正确应用待定系数法的思路,以及一定条件下的Puiseux级数范式.

Puiseux series is a mathematical tool for dynamics analysis of time-delay systems near a repeated characteristic root,and it has became a hot research topic in the recent years.This paper presents a new observation that under certain conditions,contradictions occur in calculating the Puiseux series expansion of time-delay systems when the method of undetermined coefficients is used,the reason that leads to contradictions,as well as some normal forms of the correct Puiseux series expansion under some specified conditions,are given.