{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:42:59Z","timestamp":1787319779946,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>The main result of this paper establishes that if a controller C (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant P, then global stabilization of P can also be achieved by an output feedback controller $C[h]$, where the output derivatives in C are replaced by an Euler approximation with sufficiently small delay $h&gt;0$. This is proved within the conceptual framework of the nonlinear gap metric approach to robust stability. The main result is then applied to finite dimensional linear minimum phase systems with unknown coefficients but known relative degree and known sign of the high frequency gain. Results are also given for systems with nonzero initial conditions.<\/jats:p>","DOI":"10.1137\/080726070","type":"journal-article","created":{"date-parts":[[2009,8,25]],"date-time":"2009-08-25T09:54:17Z","timestamp":1251194057000},"page":"2533-2561","source":"Crossref","is-referenced-by-count":26,"title":["Robust Stabilization by Linear Output Delay Feedback"],"prefix":"10.1137","volume":"48","author":[{"given":"Mark","family":"French","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Achim","family":"Ilchmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Markus","family":"Mueller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,8,21]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700043677"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"R. F. Curtain and H. J. Zwart,\n                      An Introduction to Infinite-Dimensional Linear Systems Theory\n                      , Texts Appl. Math. 21, Springer-Verlag, New York, 1995.","DOI":"10.1007\/978-1-4612-4224-6"},{"key":"R3","unstructured":"B. A. Francis,\n                      A Course in $H_\\infty$ Control Theory\n                      , Lecture Notes in Control and Inform. Sci. 88, Springer-Verlag, Berlin, Heidelberg, New York, 1987."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.916659"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0506336371"},{"key":"R6","unstructured":"M. French and M. Mueller,\n                      Nonlinear High Gain Separation Principles and Fast SamplingResults Ensuring Robust Stability\n                      , preprint. Available online at http:\/\/eprints.ecs.soton.ac.uk\/16885."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(89)90115-1"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211620"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1109\/9.623082"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/050641946"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2004.02.001"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/040616383"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.841137"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.828326"},{"key":"R15","unstructured":"K. Ogata,\n                      Modern Control Engineering\n                      , 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1990."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"T. J. Rivlin,\n                      An Introduction to the Approximation of Functions\n                      , Blaisdell, Waltham, MA, 1969.","DOI":"10.2307\/2004443"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"L. F. Shampine, I. Gladwell, and S. Thompson,\n                      Solving ODEs with MATLAB\n                      , Cambridge University Press, Cambridge, UK, 2003.","DOI":"10.1017\/CBO9780511615542"},{"key":"R18","unstructured":"S. Trenn,\n                      Hardy Spaces and Robustness of Linear Systems\n                      , Diplomarbeit, IlmenauUniversity of Technology, Ilmenau, Germany, 2004. Available online at http:\/\/tu-ilmenau.de\/fakmn\/Publikationen.3187.0.html."},{"key":"R19","unstructured":"K. Yosida,\n                      Functional Analysis\n                      , 6th ed., Springer-Verlag, Berlin, 1980."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080726070","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:52:05Z","timestamp":1787316725000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080726070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/080726070"],"URL":"https:\/\/doi.org\/10.1137\/080726070","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}