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Preprint 17-2004

Analysis of higher order linear differential-algebraic systems

Source file is available as :   Postscript Document

Author(s) : Volker Mehrmann , Chunchao Shi

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 17-2004

MSC 2000

65L80 Methods for differential-algebraic equations
65L05 Initial value problems

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.

Keywords : differential-algebraic equation, higher order system, order reduction, index reduction,strangeness-index, matrix polynomial

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