{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:06Z","timestamp":1787322906132,"version":"build-2736575974"},"reference-count":57,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We discuss controllability of systems that are initially given by boundary coupled PDEs of second order. These systems may be described by modules over particular rings of distributions and ultradistributions with compact support arising from the solution of the Cauchy problem of the PDE under consideration with data on the time axis. We show that those rings are B\u00e9zout domains. This property is utilized in order to derive algebraic and trajectory related controllability results.<\/jats:p>","DOI":"10.1137\/08072437x","type":"journal-article","created":{"date-parts":[[2010,4,12]],"date-time":"2010-04-12T09:40:02Z","timestamp":1271065202000},"page":"3882-3902","source":"Crossref","is-referenced-by-count":37,"title":["Controllability of Networks of Spatially One-Dimensional Second Order PDEs\u2014An Algebraic Approach"],"prefix":"10.1137","volume":"48","author":[{"given":"Frank","family":"Woittennek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hugues","family":"Mounier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,4,9]]},"reference":[{"key":"R1","unstructured":"Y. Aoustin, M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph,\n                      Theory and practice in the motion planning and control of a flexible robot arm using Mikusi\u0144ski operators\n                      , in Proceedings of the 5th Symposium on Robot Control, Nantes, France, 1997, pp. 287\u2013293."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(89)90003-1"},{"key":"R3","unstructured":"D. Breth\u00e9 and J.J. Loiseau,\n                      A result that could bear fruit for the control of delay-differential systems\n                      , in Proceedings of the 4th IEEE Mediterranean Symposium on Control Automation, Chania, Greece, 1996, pp. 168\u2013172."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"D. Breth\u00e9 and J.J. Loiseau,\n                      Proper stable factorizations for time-delay systems\n                      , in Proceedings of the 4th European Control Conference, Brussels, Belgium, 1997.","DOI":"10.23919\/ECC.1997.7082506"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(97)00113-4"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"R. Courant and D. Hilbert,\n                      Methoden der mathematischen Physik\n                      , Vol. 1, Springer-Verlag, Berlin, 1924.","DOI":"10.1007\/978-3-642-47436-1_1"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"R. Courant and D. Hilbert,\n                      Methoden der mathematischen Physik\n                      , Vol. 2, Springer-Verlag, Berlin, 1937.","DOI":"10.1007\/978-3-642-47434-7"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"R. F. Curtain and H. Zwart,\n                      An Introduction to Infinite-Dimensional Linear Systems Theory\n                      , Springer-Verlag, New York, 1995.","DOI":"10.1007\/978-1-4612-4224-6"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"R. Dager and E. Zuazua,\n                      Wave Propagation, Observation and Control in 1-d Flexible Multi-structures\n                      , Math. Appl. (Berlin) 50, Springer-Verlag, Berlin, 2006.","DOI":"10.1007\/3-540-37726-3"},{"key":"R10","unstructured":"W. F. Donoghue,\n                      Distributions and Fourier Transforms\n                      , Academic Press, New York, 1969."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(90)90062-Y"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(92)90038-T"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1080\/00207179508921959"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1998111"},{"key":"R15","first-page":"295","volume":"37","author":"Fliess M.","year":"2002","journal-title":"IMA J. Math. Control Inform.","ISSN":"https:\/\/id.crossref.org\/issn\/0265-0754","issn-type":"print"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"M. Fliess, H. Mounier, P. Rouchon, and J. Rudolph,\n                      Controllability and motion planning for linear delay systems with an application to a flexible rod\n                      , in Proceedings of the 34th IEEE Conference on Decision and Control, New Orleans, LA, 1995, pp. 2046\u20132051.","DOI":"10.1109\/CDC.1995.480649"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012995281869"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009859"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-40-00626-3"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1943-07886-X"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11860-3"},{"key":"R22","unstructured":"L. H\u00f6rmander,\n                      The Analysis of Linear Partial Differential Operators\n                      I\n                      : Distribution Theory and Fourier Analysis\n                      , Grundlehren Math. Wiss. 256, Springer-Verlag, Berlin, Heidelberg, New York, 1983."},{"key":"R23","unstructured":"L. H\u00f6rmander,\n                      The Analysis of Linear Partial Differential Operators\n                      II\n                      : Differential Operators with Constant Coefficients\n                      , Grundlehren Math. Wiss. 257, Springer-Verlag, Berlin, Heidelberg, New York, 1990."},{"key":"R24","first-page":"25","volume":"20","author":"Komatsu H.","year":"1973","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math."},{"key":"R25","first-page":"607","volume":"24","author":"Komatsu H.","year":"1973","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math."},{"key":"R26","doi-asserted-by":"crossref","unstructured":"J. Lagnese, G. Leugering, and E. J. P. G. Schmidt,\n                      Modelling, Analysis and Control of Multi-link Flexible Structures\n                      , Birkh\u00e4user, Basel, 1994.","DOI":"10.1007\/978-1-4612-0273-8"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1002\/1099-1239(20000715)10:8<629::AID-RNC502>3.0.CO;2-N"},{"key":"R28","unstructured":"B. Malgrange,\n                      Syst\u00e8mes diff\u00e9rentiels \u00e0 coefficients constants\n                      , Semin. Bourbaki, 15 (1962\/63), expos\u00e9 246."},{"key":"R29","doi-asserted-by":"crossref","unstructured":"J. Mikusi\u0144ski,\n                      Operational Calculus\n                      , Vol. 1, Pergamon Press, Oxford, UK, PWN, Warsaw, 1983.","DOI":"10.1016\/B978-0-08-025071-7.50008-2"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1515\/form.10.1.39"},{"key":"R31","unstructured":"H. Mounier, J. Rudolph, M. Petitot, and M. Fliess,\n                      A flexible rod as a linear delay system\n                      , in Proceedings of the 3rd European Control Conference, Rome, Italy, 1995, pp. 3676\u20133681."},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1007\/BF00046908"},{"key":"R33","doi-asserted-by":"crossref","unstructured":"V. P. Palamodov,\n                      Linear Differential Operators with Constant Coefficients\n                      , Springer-Verlag, New York, Berlin, 1970.","DOI":"10.1007\/978-3-642-46219-1"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900368636"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1109\/9.995037"},{"key":"R36","unstructured":"G. Picavet and M. Picavet L'Hermitte,\n                      Trigonometric polynomial rings\n                      , in Commutative Ring Theory and Applications, Lecture Notes in Pure and Appl. Math. 231, Dekker, New York, 2003, pp. 419\u2013433."},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997321784"},{"key":"R38","doi-asserted-by":"crossref","unstructured":"A. D. Polyanin,\n                      Handbook of Linear Partial Differential Equations for Engineers and Scientists\n                      , Chapman & Hall\/CRC, Boca Raton, FL, 2002.","DOI":"10.1201\/9781420035322"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1093\/imamci\/16.3.275"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012995283054"},{"key":"R41","doi-asserted-by":"crossref","unstructured":"L. Rodino,\n                      Linear Partial Differential Operators in Gevrey Spaces\n                      , World Scientific, Singapore, 1993.","DOI":"10.1142\/1550"},{"key":"R42","unstructured":"J. Rotman,\n                      An Introduction to Homological Algebra\n                      , Academic Press, Orlando, FL, 1979."},{"key":"R43","unstructured":"J. Rudolph,\n                      Beitr\u00e4ge zur flachheitsbasierten Folgeregelung linearer und nichtlinearer Systeme endlicher und unendlicher Dimension\n                      , Berichte aus der Steuerungs- und Regelungstechnik, Shaker Verlag, Aachen, 2003."},{"key":"R44","unstructured":"J. Rudolph, J. Winkler, and F. Woittennek,\n                      Flatness Based Control of Distributed Parameter Systems: Examples and Computer Exercises from Various Technological Domains\n                      , Berichte aus der Steuerungs- und Regelungstechnik, Shaker Verlag, Aachen, 2003."},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1524\/auto.2007.55.9.457"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1080\/00207170701561435"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1080\/00207170110092307"},{"key":"R48","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(01)00174-8"},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012999359718"},{"key":"R50","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(02)00285-9"},{"key":"R51","doi-asserted-by":"publisher","DOI":"10.1109\/9.73561"},{"key":"R52","doi-asserted-by":"crossref","unstructured":"F. Woittennek,\n                      Beitr\u00e4ge zum Steuerungsentwurf f\u00fcr lineare, \u00f6rtlich verteilte Systeme mit konzentrierten Stelleingriffen\n                      , Berichte aus der Steuerungs- und Regelungstechnik, Shaker Verlag, Aachen, 2007.","DOI":"10.1524\/auto.2007.55.9.497_2"},{"key":"R53","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2003020"},{"key":"R54","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008430528456"},{"key":"R55","doi-asserted-by":"crossref","unstructured":"J. Wood, E. Rogers, and D. H. Owens,\n                      Characterizing controllable n\n                      D\n                      behaviours\n                      , in Proceedings of the 36th IEEE Conference on Decision and Control, Vol. 5, 1997, pp. 4266\u20134267.","DOI":"10.1109\/CDC.1997.649506"},{"key":"R56","unstructured":"E. Zerz,\n                      Topics in Multidimensional Linear Systems Theory\n                      , Lecture Notes in Control and Inform. Sci. 256, Springer-Verlag, London, 2000."},{"key":"R57","doi-asserted-by":"publisher","DOI":"10.1080\/00207170410001726822"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/08072437X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:32:47Z","timestamp":1787319167000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/08072437X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":57,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/08072437X"],"URL":"https:\/\/doi.org\/10.1137\/08072437x","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}