Analysis and reformulation of linear delay differential-algebraic equations

General linear systems of delay differential-algebraic equations (DDAEs) of arbitrary order are studied in this paper. Under some consistency conditions, it is shown that every linear highorder 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). Condensed forms for DDAEs based on the algebraic structure of the system coefficients are derived and these forms are used 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.