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