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Main Title: Analysis of higher order linear differential-algebraic systems
Author(s): Mehrmann, Volker
Shi, Chunchao
Type: Research Paper
Abstract: We study linear over- or under-determined differential-algebraic systems of order larger than $1$. We analyze the classical procedure of turning the system into a first order system. We show that this approach leads to solutions that may have different smoothness requirements. We derive canonical and condensed forms as well as general existence and uniqueness results for differential-algebraic systems of arbitrary order and index. We also show how to identify exactly those variables for which the order reduction to first order does not lead to extra smoothness requirements. Finally we discuss some consequences for the analysis of matrix polynomials.
Subject(s): differential-algebraic equation
higher order system
order reduction
index reduction
matrix polynomial
Issue Date: 19-Jul-2004
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65L80 Methods for differential-algebraic equations
65L05 Initial value problems
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2004, 17
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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