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

Volltext

Link zum Volltext (externe URL):

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.