Linear DAEs with variable coefficients

Abstract

We characterize the class of regular linear DAEs with variable coefficients by means of admissible matrix function sequences and associated projector functions. We do not use derivative arrays; instead we generate the admissible matrix functions directly from the coefficients of the given DAE. The so-called tractability index as well as several characteristic values are attributed to each regular DAE, which generalizes the Kronecker index and the Kronecker structural data of constant matrix pencils. We provide a constructive decoupling of regular DAEs into an inherent regular ODE and a subsystem containing all differentiations. Then, with this background, a comprehensive linear DAE theory is provided, including qualitative flow properties and a rigorous description of admissible excitations. Moreover, relations to several canonical forms and other index notions are addressed.