On linear differential-algebraic equations with properly stated leading term

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