{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T01:17:13Z","timestamp":1777598233550,"version":"3.51.4"},"reference-count":30,"publisher":"Walter de Gruyter GmbH","issue":"8","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["RO 2427\/5-1"],"award-info":[{"award-number":["RO 2427\/5-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,26]]},"abstract":"<jats:title>Zusammenfassung<\/jats:title>\n               <jats:p>F\u00fcr lineare Systeme existiert eine Vielzahl von Stabilit\u00e4tskriterien, mit denen ohne gro\u00dfen Aufwand die Stabilit\u00e4t \u00fcberpr\u00fcft werden kann. Der Stabilit\u00e4tsbeweis gestaltet sich f\u00fcr nichtlineare Systeme dagegen deutlich schwieriger. Ein sehr leistungsf\u00e4higer Ansatz steht mit Lyapunovs zweiter Methode zur Verf\u00fcgung, der von LaSalle verallgemeinert wurde, und nun als das Invarianzprinzip bekannt ist. Durch eine leichte Abschw\u00e4chung der Aussage des Invarianzprinzips kann das Kriterium f\u00fcr eine geeignete Systemklasse mittels Methoden der algebraischen Geometrie \u00fcberpr\u00fcft und somit automatisiert werden. Dies erlaubt auch die Verwendung von Parametern im Ansatz der Lyapunov-Funktion oder des Systems, um beispielsweise einen Regler oder Beobachter zu parametrieren. In diesem Aufsatz werden die Methoden diskutiert und auf einige Beispiele angewandt.<\/jats:p>","DOI":"10.1515\/auto-2022-0053","type":"journal-article","created":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T09:02:42Z","timestamp":1659690162000},"page":"740-752","source":"Crossref","is-referenced-by-count":1,"title":["\u00dcber die algebraische Stabilit\u00e4tsanalyse parametrischer polynomialer Systeme mittels LaSalles Invarianzprinzip"],"prefix":"10.1515","volume":"70","author":[{"given":"Daniel","family":"Gerbet","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Regelungs- und Steuerungstheorie , 9169 Technische Universit\u00e4t Dresden , Dresden , Deutschland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"R\u00f6benack","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Regelungs- und Steuerungstheorie , 9169 Technische Universit\u00e4t Dresden , Dresden , Deutschland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,8,4]]},"reference":[{"key":"2023033111052317484_j_auto-2022-0053_ref_001","doi-asserted-by":"crossref","unstructured":"Adamy, J. 2018. 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