Characterization of classes of singular linear differential-algebraic equations

Abstract

Linear, possibly over- or underdetermined, differential-algebraic equations are studied that have the same solution behavior as linear differential-algebraic equations with well-defined strangeness index. In particular, three different characterizations are given for differential-algebraic equations, namely by means of solution spaces, canonical forms, and derivative arrays. Two levels of generalization are distinguished, where the more restrictive case contains an additional assumption on the structure of the set of consistent inhomogeneities.