{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T04:08:01Z","timestamp":1767586081755,"version":"3.37.3"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T00:00:00Z","timestamp":1687305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Internal Funds KU Leuven","award":["C14\/22\/092"],"award-info":[{"award-number":["C14\/22\/092"]}]},{"name":"Research Foundation-Flanders","award":["G092721N"],"award-info":[{"award-number":["G092721N"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,9,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The numerical minimization of the spectral abscissa function of linear time-invariant time-delay systems, an established approach to compute stabilizing controllers with a fixed structure, often gives rise to minima characterized by active characteristic roots with multiplicity higher than one. At the same time, recent theoretical results reveal situations where the so-called multiplicity induced dominancy property holds, i.e., a sufficiently high multiplicity implies that the root is dominant. Using an integrative approach, combining analytical characterizations, computation of characteristic roots and numerical optimization, a complete characterization of the stabilizability of second-order systems with input delays is provided, for both state feedback and delayed output feedback. The level sets of the minimal achievable spectral abscissa are also characterized. These results shed light on the complex relations between (configurations involving) multiple roots, the property of being dominant roots and the property of corresponding to (local\/global) minimizers of the spectral abscissa function.<\/jats:p>","DOI":"10.1093\/imamci\/dnad020","type":"journal-article","created":{"date-parts":[[2023,6,23]],"date-time":"2023-06-23T03:14:48Z","timestamp":1687490088000},"page":"403-428","source":"Crossref","is-referenced-by-count":6,"title":["A complete characterization of minima of the spectral abscissa and rightmost roots of second-order systems with input delay"],"prefix":"10.1093","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0877-0080","authenticated-orcid":false,"given":"Wim","family":"Michiels","sequence":"first","affiliation":[{"name":"Department of Computer Science, KU Leuven , 3001 Leuven , Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3444-2566","authenticated-orcid":false,"given":"Silviu-Iulian","family":"Niculescu","sequence":"additional","affiliation":[{"name":"Laboratoire des Signaux et Syst\u00e8mes, Universit\u00e9 Paris-Saclay, Inria Saclay CNRS, CentraleSup\u00e9lec , 91192 Gif-sur-Yvette , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7020-6395","authenticated-orcid":false,"given":"Islam","family":"Boussaada","sequence":"additional","affiliation":[{"name":"Institut Polytechnique des Sciences Avanc\u00e9es (IPSA) , 94200 Ivry-sur-Seine , France"},{"name":"Laboratoire des Signaux et Syst\u00e8mes, Universit\u00e9 Paris-Saclay, Inria Saclay CNRS, CentraleSup\u00e9lec , 91192 Gif-sur-Yvette , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2023,6,21]]},"reference":[{"key":"2023092216582624800_ref1","doi-asserted-by":"crossref","DOI":"10.1016\/j.ifacol.2022.09.036","article-title":"TDS-CONTROL: A MATLAB package for the analysis and controller-design of time-delay systems","volume-title":"Proceedings of the 18th IFAC Workshop on Control Applications of Optmization","author":"Appeltans","year":"2022"},{"key":"2023092216582624800_ref2","article-title":"Analysis and controller-design of time-delay systems using TDS-CONTROL. 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