DAE differential algebraic equation admissible projector function tractability index fine decoupling regularity DAE flow DAE structure Lyapunov stability canonical form index reduction Projector Based Analysis of Linear Differential Algebraic Equations René Lamour Lamour René Roswitha März März Roswitha Caren Tischendorf Tischendorf Caren Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

Projector Based Analysis of Linear Differential Algebraic Equations

René Lamour , Roswitha März , Caren Tischendorf

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
65L80 Methods for differential-algebraic equations

Abstract
We provide a comprehensive analysis of linear DAEs with continuous coefficients and properly stated leading term. We are mainly interested in so-called regular DAEs, but we address also under- and overdetermined DAEs. In particular, we describe the structured characteristic of DAEs, explain how to formulate consistent initial conditions, investigate the flow asymptotics and admissible excitations. Also, critical points are touched. We specify the main results for linear DAEs in standard form and discuss several canonical forms. We show that the constant rank conditions supporting the tractability index coincide with those applied in the strangeness index concept.

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