文章基本信息

标题：Symbolic Computation for Integro-Differential-Time-Delay Operators with Matrix Coefficients ⁎
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作者：Thomas Cluzeau ; Jamal Hossein Poor ; Alban Quadrat 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：14
页码：153-158
DOI：10.1016/j.ifacol.2018.07.215
语种：English
出版社：Elsevier
摘要：AbstractThe purpose of this paper is to algebraize and automatize computations with linear differential time-delay systems and their solutions. To this end, we explain an algebraic construction of the ring of integro-differential operators with linear substitutions having (noncommutative) matrix coefficients, which contains the ring of integro-differential-time-delay operators. Based on a reduction system for this ring, we show how such operators can be uniquely expanded into irreducible terms.Symbolic computations with these operators and their normal forms are implemented in a Mathematica package. This even allows for computations with systems having generic size and/or undetermined matrix coefficients. We illustrate how, by elementary computations with operators in this framework, results like the method of steps can be found and proven in an automated way. Normal form computations with our package can be used to partly automatize solving operator equations. As an example, we recover a generalization of Artstein’s reduction, which solves an equivalence problem of a class of differential time-delay control systems.
关键词：KeywordsDifferential time-delay systemscomputer algebraintegro-differential operators with linear substitutionsnormal formsArtstein’s reductionalgebraic analysis approach to linear systems theory