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Control Optim."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p>We study a class of integro--differential equation systems in Hilbert spaces which fits the Gurtin--Pipkin model of heat conduction with memory. Well-posedness of the system state equation is established using the operator semigroup approach. Sufficient conditions are then obtained under which infinite-time admissibility of the system observation operator follows from finite-time admissibility of the same observation operator for the associated second order Cauchy system without the first order term and convolution terms. This is done by combining the semigroup approach with the Hardy space method. An illustrative example is given, and the obtained theoretical results are verified by numerical simulations.<\/jats:p>","DOI":"10.1137\/21m1403849","type":"journal-article","created":{"date-parts":[[2022,2,16]],"date-time":"2022-02-16T08:00:45Z","timestamp":1644998445000},"page":"505-529","source":"Crossref","is-referenced-by-count":7,"title":["Infinite-Time Admissibility of the Gurtin--Pipkin Systems in Hilbert Spaces"],"prefix":"10.1137","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8087-8248","authenticated-orcid":true,"given":"Jian-Hua","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Fu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6856-2358","authenticated-orcid":true,"given":"Hua-Cheng","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"G. 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