Analysis and Reformulation of Linear Delay Differential-Algebraic Equations

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