Linear differential-algebraic equations with properly stated leading term: B -critical points
AbstractWe examine in this article 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 Π -projectors. Via a continuation of certain invariant spaces through the singularity, we arrive at a 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.