{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T13:41:13Z","timestamp":1775742073482,"version":"3.50.1"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,3,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominance of such roots compared with the spectrum localization. As a by-product of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closed-loop stability with an appropriate decay rate of the corresponding dynamical system.<\/jats:p>","DOI":"10.1093\/imamci\/dnad001","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T12:41:18Z","timestamp":1676896878000},"page":"81-105","source":"Crossref","is-referenced-by-count":15,"title":["On the pole placement of scalar linear delay systems with two delays"],"prefix":"10.1093","volume":"40","author":[{"given":"S\u00e9bastien","family":"Fueyo","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, CentraleSup\u00e9lec, Inria, Laboratoire des signaux et syst\u00e8mes , 91190 Gif-sur-Yvette , France"}]},{"given":"Guilherme","family":"Mazanti","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, CentraleSup\u00e9lec, Inria, Laboratoire des signaux et syst\u00e8mes , 91190 Gif-sur-Yvette , France"}]},{"given":"Islam","family":"Boussaada","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, CentraleSup\u00e9lec, Inria, Laboratoire des signaux et syst\u00e8mes , 91190 Gif-sur-Yvette , France"},{"name":"Institut Polytechnique des Sciences Avanc\u00e9es (IPSA) , 63 boulevard de Brandebourg, 94200 Ivry-sur-Seine , France"}]},{"given":"Yacine","family":"Chitour","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes , 91190 Gif-sur-Yvette , France"}]},{"given":"Silviu-Iulian","family":"Niculescu","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, CentraleSup\u00e9lec, Inria, Laboratoire des signaux et syst\u00e8mes , 91190 Gif-sur-Yvette , France"}]}],"member":"286","published-online":{"date-parts":[[2023,2,17]]},"reference":[{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1111\/j.1749-6632.1987.tb48740.x","article-title":"A model for the regulation of mammalian platelet production","volume":"504","author":"B\u00e9lair","year":"2006","journal-title":"Ann. New York Acad. Sci."},{"key":"2023031512451981700_","volume-title":"Differential-Difference Equations","author":"Bellman","year":"1963"},{"key":"2023031512451981700_","first-page":"01","article-title":"Stability analysis of an equation with two delays and application to the production of platelets","volume":"13","author":"Boullu","year":"2019","journal-title":"Discrete Contin Dyn Syst"},{"key":"2023031512451981700_","first-page":"196","article-title":"Partial Pole Placement via Delay Action: A Python Software for Delayed Feedback Stabilizing Design","volume-title":"ICSTCC 2020 - 24th International Conference on System Theory, Control and Computing, 2020 24th International Conference on System Theory, Control and Computing (ICSTCC), Sinaia, Romania","author":"Boussaada","year":"2020"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1051\/cocv\/2019073","article-title":"Multiplicity-induced-dominancy in parametric second-order delay differential equations: analysis and application in control design","volume":"26","author":"Boussaada","year":"2020","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.5802\/crmath.293","article-title":"The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: when delay-systems characteristics meet the zeros of kummer functions","volume":"360","author":"Boussaada","year":"(2022)","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","article-title":"Trust-region methods","volume-title":"MPS\/SIAM Series on Optimization. Society for Industrial and Applied Mathematics (SIAM)","author":"Conn","year":"2000"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6313-5","volume-title":"Functions of One Complex Variable, Volume 11 of Graduate Texts in Mathematics","author":"Conway","year":"1978"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4206-2","volume-title":"Delay Equations: Functional-, Complex-, and Nonlinear Analysis, Volume 110 of Applied Mathematical Sciences","author":"Diekmann","year":"1995"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0039-0","volume-title":"Stability of Time-Delay Systems","author":"Gu","year":"2003"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.jmaa.2005.02.034","article-title":"On stability crossing curves for general systems with two delays","volume":"311","author":"Gu","year":"2005","journal-title":"J. Math. Anal. Appl."},{"key":"2023031512451981700_","volume-title":"Differential Equations: Stability, Oscillations, Time Lags","author":"Halanay","year":"1966"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1006\/jmaa.1993.1312","article-title":"Global geometry of the stable regions for two delay differential equations","volume":"178","author":"Hale","year":"1993","journal-title":"J. Math. Anal. Appl."},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4342-7","volume-title":"Introduction to Functional Differential Equations, Volume 99 of Applied Mathematical Sciences","author":"Hale","year":"1993"},{"key":"2023031512451981700_","first-page":"s1","article-title":"Roots of the transcendental equation associated with a certain difference-differential equation","author":"Hayes","year":"1950","journal-title":"J. London Math. Soc."},{"key":"2023031512451981700_","volume-title":"An Introduction to Complex Analysis in Several Variables Volume 7 of North-Holland Mathematical Library","author":"H\u00f6rmander","year":"1990"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.automatica.2017.11.015","article-title":"Some insights into the migration of double imaginary roots under small deviation of two parameters","volume":"88","author":"Irofti","year":"2018","journal-title":"Automatica J. IFAC"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/TAC.2004.841137","article-title":"Static output feedback stabilization: necessary conditions for multiple delay controllers","volume":"50","author":"Kharitonov","year":"2005","journal-title":"IEEE Trans. Automat. Cont."},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1142\/S0218127495000570","article-title":"A geometric analysis of stability regions for a linear differential equation with two delays","volume":"5","author":"Mahaffy","year":"1995","journal-title":"Int. J. Bifurcat. Chaos"},{"key":"2023031512451981700_","first-page":"4386","article-title":"Some remarks on the regular splitting of quasi-polynomials with two delays. Characterization of double roots in degenerate cases","author":"Martinez-Gonzalez","year":"2020"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.jde.2021.03.003","article-title":"Multiplicity-induced-dominancy for delay-differential equations of retarded type","volume":"286","author":"Mazanti","year":"2021","journal-title":"J. Differential Equations"},{"key":"2023031512451981700_","first-page":"764","article-title":"Effects of roots of maximal multiplicity on the stability of some classes of delay differential-algebraic systems: the lossless propagation case","volume-title":"24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020)","author":"Mazanti","year":"2021"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611973631","article-title":"Stability, control, and computation for time-delay systems: an eigenvalue-based approach","volume-title":"Society for Industrial and Applied Mathematics (SIAM)","author":"Michiels","year":"2014"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TAC.2004.828326","article-title":"Stabilizing a chain of integrators using multiple delays","volume":"49","author":"Niculescu","year":"2004","journal-title":"IEEE Trans. Automat. Control"},{"key":"2023031512451981700_","article-title":"Cxroots: a python module to find all the roots of a complex analytic function within a given contour","author":"Parini","year":"2018"},{"key":"2023031512451981700_","volume-title":"Problems and Theorems in Analysis. I. Classics in Mathematics","author":"P\u00f3lya","year":"1998"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MCS.2010.939135","article-title":"Stability and stabilization of systems with time delay: limitations and opportunities","volume":"31","author":"Sipahi","year":"2011","journal-title":"IEEE Control Syst. Mag."},{"key":"2023031512451981700_","volume-title":"Retarded dynamical systems: stability and characteristic functions","author":"St\u00e9p\u00e1n","year":"1989"},{"key":"2023031512451981700_","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nature Methods"}],"container-title":["IMA Journal of Mathematical Control and Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/imamci\/article-pdf\/40\/1\/81\/49529117\/dnad001.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/imamci\/article-pdf\/40\/1\/81\/49529117\/dnad001.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,13]],"date-time":"2024-10-13T01:49:01Z","timestamp":1728784141000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imamci\/article\/40\/1\/81\/7043806"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,17]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,2,17]]},"published-print":{"date-parts":[[2023,3,15]]}},"URL":"https:\/\/doi.org\/10.1093\/imamci\/dnad001","relation":{},"ISSN":["0265-0754","1471-6887"],"issn-type":[{"value":"0265-0754","type":"print"},{"value":"1471-6887","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,3]]},"published":{"date-parts":[[2023,2,17]]}}}