{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:08:40Z","timestamp":1680264520777},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,7,26]]},"abstract":"<jats:title>Zusammenfassung<\/jats:title>\n               <jats:p>Dieser Beitrag behandelt die Verallgemeinerung der Backstepping-Methodik zum Entwurf von Zustandsr\u00fcckf\u00fchrungen f\u00fcr gekoppelte Diffusions-Konvektions-Reaktionssysteme auf den Fall ortsabh\u00e4ngiger Koeffizienten. F\u00fcr ein exponentiell stabiles Zielsystem mit vorgebbarer Konvergenzrate erfolgt die Herleitung der zugeh\u00f6rigen Kerngleichungen. Zu deren L\u00f6sung wird die f\u00fcr skalare parabolische Systeme bekannte Methode der sukzessiven Approximationen auf den Fall gekoppelter Systeme verallgemeinert. Dabei erfolgt sowohl die Ber\u00fccksichtigung von unterschiedlichen als auch von gleichen Diffusionskoeffizienten, womit sich ein umfassendes Bild des Backstepping-Entwurfs f\u00fcr gekoppelte parabolische Systeme ergibt. Zur Veranschaulichung der Ergebnisse des Beitrags dient ein nichtisothermer Rohrreaktor, der durch zwei verkoppelte semi-lineare parabolische PDEs beschrieben wird.<\/jats:p>","DOI":"10.1515\/auto-2018-0012","type":"journal-article","created":{"date-parts":[[2018,7,14]],"date-time":"2018-07-14T17:27:28Z","timestamp":1531589248000},"page":"558-572","source":"Crossref","is-referenced-by-count":1,"title":["Backstepping f\u00fcr gekoppelte parabolische Systeme mit ortsabh\u00e4ngigen Koeffizienten"],"prefix":"10.1515","volume":"66","author":[{"given":"Joachim","family":"Deutscher","sequence":"first","affiliation":[{"name":"Lehrstuhl f\u00fcr Regelungstechnik , Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 7 , D-91058 , Erlangen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Kerschbaum","sequence":"additional","affiliation":[{"name":"Lehrstuhl f\u00fcr Regelungstechnik , Universit\u00e4t Erlangen-N\u00fcrnberg , Cauerstra\u00dfe 7 , D-91058 , Erlangen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2018,7,13]]},"reference":[{"key":"2023033109481631011_j_auto-2018-0012_ref_001_w2aab3b7b1b1b6b1ab1c10b1Aa","doi-asserted-by":"crossref","unstructured":"A. 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