2011-07-13Buch DOI: 10.18452/2767
Linear differential-algebraic equations with properly stated leading term
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 Π-projectors. Via a continuation of certain invariant spaces through the singularity, we arrive at an scenario which accommodates both A- and Bcritical 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.
Dateien zu dieser Publikation