TECHNISCHE UNIVERSITÄT BERLIN Analysis and Reformulation of Linear Delay Di erential-Algebraic Equations

In this paper, we study general linear systems of delay di erential-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 di erential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay di erential equation (DDE). We derive condensed forms for DDAEs based on the algebraic structure of the system coe cients, and use these forms to reformulate DDAEs as strangenessfree 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.