Regular Linear Time Varying DAEs are Equivalent to DAEs in Strong Standard Canonical Form
DOI:
https://doi.org/10.52825/dae-p.v4i.2662Keywords:
Differential-Algebraic Equation, Higher Index, Regularity, Structural Analysis, Persistent Structure, Canonical Characteristic ValuesAbstract
The relationship between solvability of linear diffential-algebraic equations (DAEs) and their transformability into canonical forms has been investigated for more than forty years.
After a comparative analysis of numerous DAE frameworks the notions regularity and almost regularity were established only recently. Regular DAEs resulted to be equivalently transformable into so-called standard canonical forms (SCF) with block-structured nilpotent matrix functions featuring certain rank properties.
In this paper we prove that for regular DAEs, even an equivalent transformation into a strong standard canonical form (SSCF) is possible, i.e. a SCF with a constant nilpotent matrix. We start from block-structured SCFs and give a constructive proof.
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Copyright (c) 2026 Diana Estévez Schwarz, René Lamour, Roswitha März
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2026-06-24
Published 2026-09-16