{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:26:56Z","timestamp":1787329616713,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2019-106362GB-I00 MCIN\/AEI\/10.13039\/501100011033\/"],"award-info":[{"award-number":["PID2019-106362GB-I00 MCIN\/AEI\/10.13039\/501100011033\/"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Suomen Akatemia","doi-asserted-by":"publisher","award":["331230"],"award-info":[{"award-number":["331230"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2023,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Zeros of rational transfer function matrices [Formula: see text] are the eigenvalues of associated polynomial system matrices [Formula: see text] under minimality conditions. In this paper, we define a structured condition number for a simple eigenvalue [Formula: see text] of a (locally) minimal polynomial system matrix [Formula: see text], which in turn is a simple zero [Formula: see text] of its transfer function matrix [Formula: see text]. Since any rational matrix can be written as the transfer function of a polynomial system matrix, our analysis yields a structured perturbation theory for simple zeros of rational matrices [Formula: see text]. To capture all the zeros of [Formula: see text], regardless of whether they are poles, we consider the notion of root vectors. As corollaries of the main results, we pay particular attention to the special case of [Formula: see text] being not a pole of [Formula: see text] since in this case the results get simpler and can be useful in practice. We also compare our structured condition number with Tisseur\u2019s unstructured condition number for eigenvalues of matrix polynomials and show that the latter can be unboundedly larger. Finally, we corroborate our analysis by numerical experiments.<\/jats:p>","DOI":"10.1137\/22m1509825","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T04:23:09Z","timestamp":1693369389000},"page":"1299-1320","source":"Crossref","is-referenced-by-count":1,"title":["Perturbation Theory of Transfer Function Matrices"],"prefix":"10.1137","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1775-041X","authenticated-orcid":true,"given":"Vanni","family":"Noferini","sequence":"first","affiliation":[{"name":"Department of Mathematics and Systems Analysis, Aalto University, FI-00076, Aalto, Finland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lauri","family":"Nyman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Systems Analysis, Aalto University, FI-00076, Aalto, Finland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javier","family":"P\u00e9rez","sequence":"additional","affiliation":[{"name":"Department of Mathematical Science, University of Montana, Missoula, MT 59812 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3655-8690","authenticated-orcid":true,"given":"Mar\u00eda C.","family":"Quintana","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Mathematics and Systems Analysis, Aalto University, PO Box 11100, FI-00076, Aalto, Finland."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,8,30]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/0614061"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1145\/2427023.2427024"},{"key":"ref3","unstructured":"M. Dahleh , \nM. A. Dahleh , and \nG. 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