Singularities of linear time-varying DAEs

Abstract

Singular issues arising in linear time-varying differential-algebraic equations are addressed in this paper. We review the use of projector methods based upon the tractability index concept for the analysis of regular problems. A taxonomy of singularities which describes the failing of some assumption in the tractability index definition is then introduced. The analysis of singular problems is focused on situations in which the degeneracy is a minimal one, namely, equations which admit a well-defined extension of the solution set through the singularity. In this framework, so-called weak singularities are shown to display a non-singular local flow despite the singular nature of the problem, extending previous results proved for low-index autonomous systems. Several examples illustrate the scope of the work.