On linear differential-algebraic equations with properly stated leading term. II: Critical points

Roswitha März , Ricardo Riaza

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

MSC 2000

34A09 Implicit equations, differential-algebraic equations

34A30 Linear equations and systems, general

Abstract
This paper addresses critical points of linear differential-algebraic equations (DAEs) of the form A(t)(D(t)x(t))' + B(t)x(t) = q(t) within a projector-based framework. We present a taxonomy of critical points which reflects the phenomenon from which the singularity stems; this taxonomy is proved independent of projectors and also invariant under linear time-varying coordinate changes and refactorizations. Under certain working assumptions, the analysis of such critical problems can be carried out though a scalarly implicit decoupling, and certain harmless problems in which such decoupling can be rewritten in explicit form are characterized. A linear, time-varying analogue of Chua's circuit is discussed with illustrative purposes.