Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915228897247232 |
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| author | Schwarz, Diana Estévez Lamour, René März, Roswitha |
| author_facet | Schwarz, Diana Estévez Lamour, René März, Roswitha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form Schwarz, Diana Estévez Lamour, René März, Roswitha Rings and Algebras Classical Analysis and ODEs 34A09, 34A12, 34A30 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. |
| title | Regular linear time varying DAEs are equivalent to DAEs in strong standard canonical form |
| topic | Rings and Algebras Classical Analysis and ODEs 34A09, 34A12, 34A30 |
| url | https://arxiv.org/abs/2504.03658 |