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Bibliographic Details
Main Author: Bock, Alexander Samuel
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.07043
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author Bock, Alexander Samuel
author_facet Bock, Alexander Samuel
contents This paper presents a framework for local solutions to time-varying linear differential-algebraic equations (DAEs) with real meromorphic coefficients. The local solutions on compact intervals form a sheaf. This permits a simple definition of controllability in the sense of Jan C. Willems. We prove that this notion is equivalent to the established global notion by giving an algebraic characterization based on the Teichmüller-Nakayama form. Finally, we study conditions under which local solutions admit extension, which is necessary for controllability.
format Preprint
id arxiv_https___arxiv_org_abs_2604_07043
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On local solutions to time-varying linear DAEs
Bock, Alexander Samuel
Dynamical Systems
34A09 (Primary), 93B05, 93C05, 93B25 (Secondary)
This paper presents a framework for local solutions to time-varying linear differential-algebraic equations (DAEs) with real meromorphic coefficients. The local solutions on compact intervals form a sheaf. This permits a simple definition of controllability in the sense of Jan C. Willems. We prove that this notion is equivalent to the established global notion by giving an algebraic characterization based on the Teichmüller-Nakayama form. Finally, we study conditions under which local solutions admit extension, which is necessary for controllability.
title On local solutions to time-varying linear DAEs
topic Dynamical Systems
34A09 (Primary), 93B05, 93C05, 93B25 (Secondary)
url https://arxiv.org/abs/2604.07043