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Main Title: Distance problems for dissipative Hamiltonian systems and related matrix polynomials
Author(s): Mehl, Christian
Mehrmann, Volker
Wojtylak, Michal
Type: Research Paper
Abstract: We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an important question whether a given model is close to a 'bad' model that could be considered as ill-posed or singular. This is usually done by computing a distance to the nearest model with such properties. We will discuss the distance to singularity and the distance to the nearest high index problem for dissipative Hamiltonian systems. While for general unstructured differential-algebraic systems the characterization of these distances are partially open problems, we will show that for dissipative Hamiltonian systems and related matrix polynomials there exist explicit characterizations that can be implemented numerically.
Subject(s): distance to singularity
distance to high index problem
distance to instability
dissipative Hamiltonian system
differential-algebraic system
matrix pencil
Kronecker canonical form
Issue Date: 24-Jan-2020
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2020, 01
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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