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Viele der hierbei betrachteten Anwendungen lassen sich nach einer geeigneten regelungsorientierten Modellbildung sowie gegebenenfalls nach einer Zustandstransformation in Form von gew\u00f6hnlichen Differentialgleichungssystemen mit einem dominierenden linearen Anteil beschreiben, wobei nichtlineare Effekte nicht vollst\u00e4ndig vernachl\u00e4ssigt werden sollten. F\u00fcr die Berechnung gesicherter Zustandseinschl\u00fcsse lassen sich beispielsweise allgemeine Ans\u00e4tze basierend auf Taylor-Reihenentwicklungen der zu bestimmenden L\u00f6sungen heranziehen. Diese allgemeinen Ans\u00e4tze nutzen jedoch in der Regel kein Vorwissen \u00fcber systemspezifische Eigenschaften wie quasi-lineare Dynamik oder Stabilit\u00e4t. Um diese Eigenschaften in der Praxis effizient nutzbar zu machen, wird im Rahmen dieser Arbeit ein Exponentialansatz zur Berechnung garantierter L\u00f6sungseinschl\u00fcsse f\u00fcr Systeme gew\u00f6hnlicher Differentialgleichungen hergeleitet, der ausgehend von einer reellwertigen Implementierung f\u00fcr Systeme mit aperiodischer Dynamik auf die Berechnung komplexwertiger Zustandseinschl\u00fcsse f\u00fcr Prozesse mit oszillatorischem Verhalten verallgemeinert wird. Zum Abschluss werden M\u00f6glichkeiten vorgestellt, die entwickelten Verfahren auf Systeme von fraktionalen Differentialgleichungen auszudehnen.<\/jats:p>","DOI":"10.1515\/auto-2019-0065","type":"journal-article","created":{"date-parts":[[2020,9,23]],"date-time":"2020-09-23T07:46:57Z","timestamp":1600847217000},"page":"826-839","source":"Crossref","is-referenced-by-count":0,"title":["Intervallmethoden zur Berechnung exponentieller Zustandseinschl\u00fcsse f\u00fcr die Erreichbarkeitsanalyse unsicherer Systeme"],"prefix":"10.1515","volume":"68","author":[{"given":"Andreas","family":"Rauh","sequence":"first","affiliation":[{"name":"Lehrstuhl f\u00fcr Mechatronik , 12971 Universit\u00e4t Rostock , Justus-von-Liebig-Weg 6 , Rostock , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julia","family":"Kersten","sequence":"additional","affiliation":[{"name":"Lehrstuhl f\u00fcr Mechatronik , 12971 Universit\u00e4t Rostock , Justus-von-Liebig-Weg 6 , Rostock , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ekaterina","family":"Auer","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Elektrotechnik & Informatik , Hochschule Wismar , Philipp-M\u00fcller-Str. 14 , D-23966 Wismar , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harald","family":"Aschemann","sequence":"additional","affiliation":[{"name":"Lehrstuhl f\u00fcr Mechatronik , 12971 Universit\u00e4t Rostock , Justus-von-Liebig-Weg 6 , Rostock , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,9,22]]},"reference":[{"key":"2023033109544156829_j_auto-2019-0065_ref_001_w2aab3b7b1b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Amairi, M., M. 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