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Bei totzeitfreien gew\u00f6hnlichen Differentialgleichungen lassen sich Untermengen des Einzugsbereichs durch Subniveaumengen von Lyapunov-Funktionen beschreiben. Im Gegensatz dazu kann bei totzeitbehafteten Systemen gegebenenfalls keine nichtleere Subniveaumenge eines entsprechenden Lyapunov-Krasovskii-Funktionals in das Monotoniegebiet einbeschrieben werden. Der vorliegende Beitrag gibt zul\u00e4ssige Einschr\u00e4nkungen der Subniveaumengen an, um dieses Problem zu l\u00f6sen. Zudem werden numerische Methoden beschrieben, die auf Oberschranken des Einzugsradius schlie\u00dfen lassen.<\/jats:p>","DOI":"10.1515\/auto-2020-0034","type":"journal-article","created":{"date-parts":[[2020,8,18]],"date-time":"2020-08-18T07:24:43Z","timestamp":1597735483000},"page":"667-686","source":"Crossref","is-referenced-by-count":0,"title":["Grundprinzipien f\u00fcr die Absch\u00e4tzung von Einzugsbereichen in Totzeitsystemen"],"prefix":"10.1515","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1938-381X","authenticated-orcid":false,"given":"Tessina H.","family":"Scholl","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Automation und angewandte Informatik , Karlsruher Institut f\u00fcr Technologie (KIT) , Hermann-von-Helmholtz-Platz 1 , Eggenstein-Leopoldshafen , Deutschland"}]},{"given":"Veit","family":"Hagenmeyer","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Automation und angewandte Informatik , Karlsruher Institut f\u00fcr Technologie (KIT) , Hermann-von-Helmholtz-Platz 1 , Eggenstein-Leopoldshafen , Deutschland"}]},{"given":"Lutz","family":"Gr\u00f6ll","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Automation und angewandte Informatik , Karlsruher Institut f\u00fcr Technologie (KIT) , Hermann-von-Helmholtz-Platz 1 , Eggenstein-Leopoldshafen , Deutschland"}]}],"member":"374","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"2023033110252782502_j_auto-2020-0034_ref_001_w2aab3b7e1433b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"D. 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