Preprint 08-2012

Analysis and Reformulation of Linear Delay Differential-Algebraic Equations

Author(s) : Phi Ha , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 08-2012

MSC 2000

34A09 Implicit equations, differential-algebraic equations

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract :
In this paper, we study general linear systems of delay differential-algebraic equations (DDAEs) of arbitrary order. We show that under some consistency conditions, every linear high-order DAE can be reformulated as an underlying high-order ordinary differential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay differential equation (DDE). We derive condensed forms for DDAEs based on the algebraic structure of the system coefficients, and use these forms to reformulate DDAEs as strangeness-free systems, where all constraints are explicitly available. The condensed forms are also used to investigate structural properties of the system like solvability, regularity, consistency and smoothness requirements.

Keywords : Delay differential-algebraic equation, differential-algebraic equation, strangeness-index, regularization, index reduction