{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T01:51:32Z","timestamp":1787363492632,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>This paper deals with frequency domain robust regulation of signals generated by an infinite-dimensional exosystem. The problem is formulated and the stability types are chosen so that one can generalize the existing finite-dimensional theory to more general classes of infinite-dimensional systems and signals. The main results of this article are extensions of the internal model principle, of a necessary and sufficient solvability condition for the robust regulation problem, and of Davison's simple servo compensator for stable plants in the chosen algebraic framework.<\/jats:p>","DOI":"10.1137\/130950057","type":"journal-article","created":{"date-parts":[[2015,1,13]],"date-time":"2015-01-13T11:53:38Z","timestamp":1421150018000},"page":"139-166","source":"Crossref","is-referenced-by-count":10,"title":["Frequency Domain Robust Regulation of Signals Generated by an Infinite-Dimensional Exosystem"],"prefix":"10.1137","volume":"53","author":[{"given":"Petteri","family":"Laakkonen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Seppo","family":"Pohjolainen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,1,13]]},"reference":[{"key":"atypb1","unstructured":"M. K. P. Bhat,\n                      Regulator Theory for Evolution Systems\n                      , Ph.D. thesis, University of Toronto, Canada, 1976."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1978.1084544"},{"key":"atypb3","first-page":"7","volume":"94","author":"Callier F. M.","year":"1980","journal-title":"Ann. Soc. Sci. Bruxelles"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"R. F. Curtain and H. J. 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":"atypb5","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1976.1101126"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1976.1101137"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(75)90022-9"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1980.1102374"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01447855"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/0315033"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(83)90078-X"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1080\/00207177508922111"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/9.847722"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/090757976"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1109\/9.1274"},{"key":"atypb16","unstructured":"R. A. Horn and C. R. Johnson,\n                      Matrix Analysis\n                      , Cambridge University Press, Cambridge, UK, 1999."},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"J. Huang,\n                      Nonlinear Output Regulation: Theory and Applications\n                      , SIAM, Philadelphia, 2004.","DOI":"10.1137\/1.9780898718683"},{"key":"atypb18","unstructured":"E. Immonen,\n                      State Space Output Regulation Theory for Infinite-Dimensional Linear Systems and Bounded Uniformly Continuous Exogenous Signals\n                      , Ph.D. thesis, Tampere University of Technology, Tampere, Finland, 2006."},{"key":"atypb19","unstructured":"T. Inoue, M. Nakano, and S. Iwai,\n                      High accuracy control of servomechanism for repeated contouring\n                      , in Proceedings of the 10th Annual Symposium on Incremental Motion Control Systems and Devices, 1981, pp. 285-292."},{"key":"atypb20","first-page":"826","volume":"5","author":"Kitano H.","year":"2004","journal-title":"Nature"},{"key":"atypb21","unstructured":"Z. X. L. Cuiyan and Z. Dongchun,\n                      Theory and applications of the repetitive control\n                      , in Proceedings of the SICE Annual Conference, Hokkaido Institute of Technology, Sapporo, Japan, 2004."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1080\/00207179.2011.572999"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"P. Laakkonen and S. Pohjolainen,\n                      Solvability of the output regulation problem with a feedforward controller\n                      , in Proceedings of 12th European Control Conference (ECC) 2013, Zu\u0308rich, Switzerland, 2013.","DOI":"10.23919\/ECC.2013.6669179"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"H. Logemann,\n                      Stabilization and regulation of infinite-dimensional systems using coprime factorizations\n                      , in Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems, R. Curtain, A. Bensoussan, and J. Lions, eds., Lecture Notes in Control and Inform. Sci. 185, Springer-Verlag, Berlin, 1993, pp. 102-139.","DOI":"10.1007\/BFb0115022"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.825618"},{"key":"atypb26","unstructured":"C. N. Nett,\n                      The fractional representation approach to robust linear feedback design: A self-contained exposition\n                      , M.S. thesis, Rensselaer Polytechnic Institute, Troy, NY, 1984."},{"key":"atypb27","unstructured":"L. Paunonen,\n                      Output Regulation Theory for Linear Systems with Infinite-Dimensional and Periodic Exosystems\n                      , Ph.D. thesis, Tampere University of Technology, Tampere, Finland, 2011."},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2013.01.005"},{"key":"atypb29","unstructured":"L. Paunonen and P. Laakkonen,\n                      On polynomial stability for linear systems\n                      , in Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, 2014."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/090760957"},{"key":"atypb31","first-page":"702","volume":"24","author":"Paunonen L.","year":"2012","journal-title":"Internat. J. Robust Nonlinear Control"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1982.1102887"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012902417139"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1007\/s00498-005-0160-9"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(03)00192-4"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1080\/00207178508933421"},{"key":"atypb37","unstructured":"M. Vidyasagar,\n                      Control System Synthesis: A Factorization Approach\n                      , MIT Press, Cambridge, MA, 1985."},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1982.1103015"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(99)00036-9"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(92)90009-5"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1080\/00207170500390903"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130950057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:20:39Z","timestamp":1787318439000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130950057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130950057"],"URL":"https:\/\/doi.org\/10.1137\/130950057","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}