{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T11:47:54Z","timestamp":1767181674270,"version":"build-2238731810"},"reference-count":34,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR 15-CE40.0010"],"award-info":[{"award-number":["ANR 15-CE40.0010"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we consider control systems for which the underlying semigroup is analytic, and the resolvent of its generator is compact. In that case we give a characterization of the stabilizability of such control systems. When the stabilizability condition is satisfied the system is also stabilizable by finite-dimensional controls.\nWe end the paper by giving an application of this result to the stabilizability of the Oseen equations with mixed boundary conditions.<\/jats:p>","DOI":"10.1515\/cmam-2018-0031","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T12:45:03Z","timestamp":1531399503000},"page":"797-811","source":"Crossref","is-referenced-by-count":9,"title":["Stabilizability of Infinite-Dimensional Systems by Finite-Dimensional Controls"],"prefix":"10.1515","volume":"19","author":[{"given":"Jean-Pierre","family":"Raymond","sequence":"first","affiliation":[{"name":"IMT , UMR 5219 , Universit\u00e9 Paul Sabatier Toulouse III and CNRS , 31062 Toulouse Cedex , France"}]}],"member":"374","published-online":{"date-parts":[[2018,7,7]]},"reference":[{"key":"2023033110105340859_j_cmam-2018-0031_ref_001_w2aab3b7e2422b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"C.  Airiau, J.-M.  Buchot, R. K.  Dubey, M.  Fourni\u00e9, J.-P.  Raymond and J.  Weller-Calvo,\nStabilization and best actuator location for the Navier\u2013Stokes equations,\nSIAM J. Sci. Comput. 39 (2017), no. 5, B993\u2013B1020.","DOI":"10.1137\/16M107503X"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_002_w2aab3b7e2422b1b6b1ab2ab2Aa","unstructured":"H.  Amann,\nFeedback stabilization of linear and semilinear parabolic systems,\nSemigroup Theory and Applications (Trieste 1987),\nLecture Notes Pure Appl. Math. 116,\nDekker, New York (1989), 21\u201357."},{"key":"2023033110105340859_j_cmam-2018-0031_ref_003_w2aab3b7e2422b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"L.  Amodei and J.-M.  Buchot,\nA stabilization algorithm of the Navier\u2013Stokes equations based on algebraic Bernoulli equation,\nNumer. Linear Algebra Appl. 19 (2012), no. 4, 700\u2013727.","DOI":"10.1002\/nla.799"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_004_w2aab3b7e2422b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"M.  Badra,\nFeedback stabilization of the 2-D and 3-D Navier\u2013Stokes equations based on an extended system,\nESAIM Control Optim. Calc. Var. 15 (2009), no. 4, 934\u2013968.","DOI":"10.1051\/cocv:2008059"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_005_w2aab3b7e2422b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"M.  Badra,\nLyapunov function and local feedback boundary stabilization of the Navier\u2013Stokes equations,\nSIAM J. Control Optim. 48 (2009), no. 3, 1797\u20131830.","DOI":"10.1137\/070682630"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_006_w2aab3b7e2422b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"M.  Badra,\nAbstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier\u2013Stokes and Boussinesq\nequations with Neumann or Dirichlet control,\nDiscrete Contin. Dyn. Syst. 32 (2012), no. 4, 1169\u20131208.","DOI":"10.3934\/dcds.2012.32.1169"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_007_w2aab3b7e2422b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"M.  Badra and T.  Takahashi,\nStabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers: Application to the Navier\u2013Stokes system,\nSIAM J. Control Optim. 49 (2011), no. 2, 420\u2013463.","DOI":"10.1137\/090778146"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_008_w2aab3b7e2422b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"M.  Badra and T.  Takahashi,\nOn the Fattorini criterion for approximate controllability and stabilizability of parabolic systems,\nESAIM Control Optim. Calc. Var. 20 (2014), no. 3, 924\u2013956.","DOI":"10.1051\/cocv\/2014002"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_009_w2aab3b7e2422b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"V.  Barbu,\nStabilization of Navier\u2013Stokes Flows,\nComm. Control Engrg. Ser.,\nSpringer, London, 2011.","DOI":"10.1007\/978-0-85729-043-4"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_010_w2aab3b7e2422b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"V.  Barbu, I.  Lasiecka and R.  Triggiani,\nTangential boundary stabilization of Navier\u2013Stokes equations,\nMem. Amer. Math. Soc. 181 (2006), Paper No. 852.","DOI":"10.1090\/memo\/0852"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_011_w2aab3b7e2422b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"C. D.  Benchimol,\nA note on weak stabilizability of contraction semigroups,\nSIAM J. Control Optim. 16 (1978), no. 3, 373\u2013379.","DOI":"10.1137\/0316023"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_012_w2aab3b7e2422b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"A.  Bensoussan, G.  Da Prato, M. C.  Delfour and S. K.  Mitter,\nRepresentation and Control of Infinite-Dimensional Systems. Vol. 2,\nSystems Control Found. Appl.,\nBirkh\u00e4user, Boston, 1993.","DOI":"10.1007\/978-1-4612-2750-2"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_013_w2aab3b7e2422b1b6b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"C.  Fabre and G.  Lebeau,\nProlongement unique des solutions de l\u2019equation de Stokes,\nComm. Partial Differential Equations 21 (1996), no. 3\u20134, 573\u2013596.","DOI":"10.1080\/03605309608821198"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_014_w2aab3b7e2422b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"H. O.  Fattorini,\nSome remarks on complete controllability,\nSIAM J. Control 4 (1966), 686\u2013694.","DOI":"10.1137\/0304048"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_015_w2aab3b7e2422b1b6b1ab2ac15Aa","doi-asserted-by":"crossref","unstructured":"H. O.  Fattorini,\nOn complete controllability of linear systems,\nJ. Differential Equations 3 (1967), 391\u2013402.","DOI":"10.1016\/0022-0396(67)90039-3"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_016_w2aab3b7e2422b1b6b1ab2ac16Aa","unstructured":"M.  Fourni\u00e9, M.  Ndiaye and J.-P.  Raymond,\nFeedback stabilization of a two-dimensional fluid-structure intercation system with mixed boundary conditions,\npreprint (2018), https:\/\/hal.archives-ouvertes.fr\/hal-01743783."},{"key":"2023033110105340859_j_cmam-2018-0031_ref_017_w2aab3b7e2422b1b6b1ab2ac17Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Fursikov,\nStabilizability of a quasilinear parabolic equation by means of boundary feedback control,\nMat. Sb. 192 (2001), no. 4, 115\u2013160.","DOI":"10.1070\/SM2001v192n04ABEH000560"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_018_w2aab3b7e2422b1b6b1ab2ac18Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Fursikov,\nStabilizability of two-dimensional Navier\u2013Stokes equations with help of a boundary feedback control,\nJ. Math. Fluid Mech. 3 (2001), no. 3, 259\u2013301.","DOI":"10.1007\/PL00000972"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_019_w2aab3b7e2422b1b6b1ab2ac19Aa","doi-asserted-by":"crossref","unstructured":"A. V.  Fursikov,\nStabilization for the 3D Navier\u2013Stokes system by feedback boundary control,\nDiscrete Contin. Dyn. Syst. 10 (2004), no. 1\u20132, 289\u2013314.","DOI":"10.3934\/dcds.2004.10.289"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_020_w2aab3b7e2422b1b6b1ab2ac20Aa","doi-asserted-by":"crossref","unstructured":"T.  Kato,\nPerturbation Theory for Linear Operators,\nClassics Math.,\nSpringer, Berlin, 1995.","DOI":"10.1007\/978-3-642-66282-9"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_021_w2aab3b7e2422b1b6b1ab2ac21Aa","doi-asserted-by":"crossref","unstructured":"I.  Lasiecka and R.  Triggiani,\nStabilization and structural assignment of Dirichlet boundary feedback parabolic equations,\nSIAM J. Control Optim. 21 (1983), no. 5, 766\u2013803.","DOI":"10.1137\/0321047"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_022_w2aab3b7e2422b1b6b1ab2ac22Aa","doi-asserted-by":"crossref","unstructured":"I.  Lasiecka and R.  Triggiani,\nThe regulator problem for parabolic equations with Dirichlet boundary control. II. Galerkin approximation,\nAppl. Math. Optim. 16 (1987), no. 3, 187\u2013216.","DOI":"10.1007\/BF01442191"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_023_w2aab3b7e2422b1b6b1ab2ac23Aa","unstructured":"I.  Lasiecka and R.  Triggiani,\nStability and Stabilizability of Infinite Dimensional Systems. Vol. 1,\nCambridge University Press, Cambridge, 2000."},{"key":"2023033110105340859_j_cmam-2018-0031_ref_024_w2aab3b7e2422b1b6b1ab2ac24Aa","unstructured":"D.  Maity, J.-P.  Raymond and A.  Roy,\nLocal-in-time existence of strong solutions to a 3D fluid-structure intercation model,\npreprint (2018)."},{"key":"2023033110105340859_j_cmam-2018-0031_ref_025_w2aab3b7e2422b1b6b1ab2ac25Aa","doi-asserted-by":"crossref","unstructured":"V.  Maz\u2019ya and J.  Rossmann,\nElliptic Equations in Polyhedral Domains,\nMath. Surveys Monogr. 162,\nAmerican Mathematical Society, Providence, 2010.","DOI":"10.1090\/surv\/162"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_026_w2aab3b7e2422b1b6b1ab2ac26Aa","doi-asserted-by":"crossref","unstructured":"T.  Nambu,\nOn the stabilization of diffusion equations: boundary observation and feedback,\nJ. Differential Equations 52 (1984), no. 2, 204\u2013233.","DOI":"10.1016\/0022-0396(84)90177-3"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_027_w2aab3b7e2422b1b6b1ab2ac27Aa","doi-asserted-by":"crossref","unstructured":"P. A.  Nguyen and J.-P.  Raymond,\nBoundary stabilization of the Navier\u2013Stokes equations in the case of mixed boundary conditions,\nSIAM J. Control Optim. 53 (2015), no. 5, 3006\u20133039.","DOI":"10.1137\/13091364X"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_028_w2aab3b7e2422b1b6b1ab2ac28Aa","doi-asserted-by":"crossref","unstructured":"A. J.  Pritchard and J.  Zabczyk,\nStability and stabilizability of infinite-dimensional systems,\nSIAM Rev. 23 (1981), no. 1, 25\u201352.","DOI":"10.1137\/1023003"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_029_w2aab3b7e2422b1b6b1ab2ac29Aa","doi-asserted-by":"crossref","unstructured":"J.-P.  Raymond,\nFeedback boundary stabilization of the two-dimensional Navier\u2013Stokes equations,\nSIAM J. Control Optim. 45 (2006), no. 3, 790\u2013828.","DOI":"10.1137\/050628726"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_030_w2aab3b7e2422b1b6b1ab2ac30Aa","doi-asserted-by":"crossref","unstructured":"J.-P.  Raymond,\nFeedback boundary stabilization of the three-dimensional incompressible Navier\u2013Stokes equations,\nJ. Math. Pures Appl. (9) 87 (2007), no. 6, 627\u2013669.","DOI":"10.1016\/j.matpur.2007.04.002"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_031_w2aab3b7e2422b1b6b1ab2ac31Aa","doi-asserted-by":"crossref","unstructured":"J.-P.  Raymond,\nStokes and Navier\u2013Stokes equations with nonhomogeneous boundary conditions,\nAnn. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire 24 (2007), no. 6, 921\u2013951.","DOI":"10.1016\/j.anihpc.2006.06.008"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_032_w2aab3b7e2422b1b6b1ab2ac32Aa","doi-asserted-by":"crossref","unstructured":"J.-P.  Raymond and L.  Thevenet,\nBoundary feedback stabilization of the two dimensional Navier\u2013Stokes equations with finite dimensional controllers,\nDiscrete Contin. Dyn. Syst. 27 (2010), no. 3, 1159\u20131187.","DOI":"10.3934\/dcds.2010.27.1159"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_033_w2aab3b7e2422b1b6b1ab2ac33Aa","doi-asserted-by":"crossref","unstructured":"R.  Triggiani,\nOn the stabilizability problem in Banach space,\nJ. Math. Anal. Appl. 52 (1975), no. 3, 383\u2013403.","DOI":"10.1016\/0022-247X(75)90067-0"},{"key":"2023033110105340859_j_cmam-2018-0031_ref_034_w2aab3b7e2422b1b6b1ab2ac34Aa","unstructured":"M.  Tucsnak and G.  Weiss,\nMathematical Control Theory. An Introduction,\nMod. Birkh\u00e4user Class.,\nBirkh\u00e4user, Basel, 2009."}],"updated-by":[{"DOI":"10.1515\/cmam-2020-2033","type":"retraction","label":"Retraction","source":"retraction-watch","updated":{"date-parts":[[2020,3,28]],"date-time":"2020-03-28T00:00:00Z","timestamp":1585353600000},"record-id":"23063"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/19\/4\/article-p797.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0031\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0031\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T07:23:30Z","timestamp":1680247410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0031\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,7]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4,10]]},"published-print":{"date-parts":[[2019,10,1]]}},"alternative-id":["10.1515\/cmam-2018-0031"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2018-0031","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2018,7,7]]}}}