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arXiv · 2504.03658

Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form

Diana Estévez Schwarz·René Lamour·Roswitha März
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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.

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Diana Estévez Schwarz, René Lamour, Roswitha März. 2025-03-07. Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form. https://arxiv.org/abs/2504.03658

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