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On norm-based estimations for domains of attraction in nonlinear time-delay systems

Scholl, Tessina H. 1; Hagenmeyer, Veit 1; Gröll, Lutz 1
1 Institut für Automation und angewandte Informatik (IAI), Karlsruher Institut für Technologie (KIT)


For nonlinear time-delay systems, domains of attraction are rarely studied despite their importance for technological applications. The present paper provides methodological hints for the determination of an upper bound on the radius of attraction by numerical means. Thereby, the respective Banach space for initial functions has to be selected and primary initial functions have to be chosen. The latter are used in time-forward simulations to determine a first upper bound on the radius of attraction. Thereafter, this upper bound is refined by secondary initial functions, which result a posteriori from the preceding simulations. Additionally, a bifurcation analysis should be undertaken. This analysis results in a possible improvement of the previous estimation. An example of a time-delayed swing equation demonstrates the various aspects.

Verlagsausgabe §
DOI: 10.5445/IR/1000119161
Veröffentlicht am 10.06.2020
DOI: 10.1007/s11071-020-05620-8
Zitationen: 9
Web of Science
Zitationen: 6
Zitationen: 10
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Automation und angewandte Informatik (IAI)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 0924-090X, 1573-269X
KITopen-ID: 1000119161
HGF-Programm 37.06.01 (POF III, LK 01) Networks and Storage Integration
Erschienen in Nonlinear dynamics
Verlag Springer
Band 100
Seiten 2027–2045
Vorab online veröffentlicht am 07.05.2020
Nachgewiesen in Dimensions
Web of Science
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