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Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization

Title data

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

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

Official URL: Volltext

Project information

Project financing: Andere

Abstract in another language

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.

Further data

Item Type: Book / Monograph
Refereed: Yes
Keywords: dynamical system; control system; long time behaviour; discretization; attractor; domain of attraction; convergence rate
Subject classification: Mathematics Subject Classification Code: 37B25 93D30 65P40 93B05 93B35 49L25
ISSN der Serie: 0075-8434
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 16 Nov 2018 07:46
Last Modified: 16 Nov 2018 07:46
URI: https://eref.uni-bayreuth.de/id/eprint/46326