  We introduce a framework for the description of a large class of
delay-differential algebraic systems, in which we study three core problems:
first we characterize abstractly the well-posedness of the initial-value
problem, then we design a practical test for well-posedness based on a
graph-theoretic representation of the system; finally, we provide a general
stability criterion. We apply each of these results to a structure that
commonly arises in the control of delay systems.
