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Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization

Titelangaben

Grüne, Lars:
Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization.
Berlin : Springer , 2002 . - 235 S. - (Lecture Notes in Mathematics ; 1783 )
ISBN 978-3-540-43391-0

Rez.:


DOI: https://doi.org/10.1007/b83677

Volltext

Link zum Volltext (externe URL): Volltext

Abstract

In this monograph we to investigate several aspects of long time or asymptotic behavior under perturbations and numerical discretization. More precisely, we consider asymptotically stable attracting sets, attractors and their respective domains of attraction. We will do this not only for classical dynamical systems (as induced, e.g., by the solutions of an autonomous ordinary differential equation), but also for systems with inputs, i.e., control systems or systems subject to some perturbation, for which these "asymptotic objects" can be generalized in a natural way. We investigate several techniques, which on the one hand allow us to conclude convergence (and related convergence rates) of the numerical approximations of these sets and on the other hand help identifying the cases in which convergence does not hold. Novel algorithms based on the analytical results are also presented.

Weitere Angaben

Publikationsform: Buch / Monografie
Begutachteter Beitrag: Ja
Keywords: Dynamical system; Control system; Long time behaviour; Discretization; Attractor; domain of attraction; Convergence rate
Fachklassifikationen: Mathematics Subject Classification Code: 37B25 93D30 65P40 93B05 93B35 49L25
ISSN der Serie: 0075-8434
Institutionen der Universität: Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) > Lehrstuhl Mathematik V (Angewandte Mathematik) - Univ.-Prof. Dr. Lars Grüne
Profilfelder
Profilfelder > Advanced Fields
Profilfelder > Advanced Fields > Nichtlineare Dynamik
Titel an der UBT entstanden: Nein
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 16 Nov 2018 07:46
Letzte Änderung: 09 Jan 2024 12:56
URI: https://eref.uni-bayreuth.de/id/eprint/46326