Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form
Abstract
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 a transformation into a strong standard canonical form (SSCF) is possible, i.e. a SCF with a constant nilpotent matrix. We start from block-structured SCF and give a constructive proof.
Keywords
Cite
@article{arxiv.2504.03658,
title = {Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form},
author = {Diana Estévez Schwarz and René Lamour and Roswitha März},
journal= {arXiv preprint arXiv:2504.03658},
year = {2025}
}
Comments
14 pages, 10 figures