Linear differential-algebraic equations with properly stated leading term: B-critical points

Roswitha März , Ricardo Riaza

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 0709, 15 pages

MSC 2000

34A09 Implicit equations, differential-algebraic equations

34A30 Linear equations and systems, general

Abstract
We examine in this paper so-called B-critical points of linear, time-varying differential-algebraic equations (DAEs) of the form A(t)(D(t)x(t))'+B(t)x(t)=q(t). These critical or singular points, which cannot be handled by classical projector methods, require adapting a recently introduced framework based on $\Pi$-projectors. Via a continuation of certain invariant spaces through the singularity, we arrive at an scenario which accommodates both A- and B-critical DAEs.The working hypotheses apply in particular to standard-form analytic systems although, in contrast to other approaches to critical problems, the scope of our approach extends beyond the analytic setting. Some examples illustrate the results.