{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:07:38Z","timestamp":1762520858648},"reference-count":30,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[2003,11,1]],"date-time":"2003-11-01T00:00:00Z","timestamp":1067644800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems & Control Letters"],"published-print":{"date-parts":[[2003,11]]},"DOI":"10.1016\/s0167-6911(03)00169-5","type":"journal-article","created":{"date-parts":[[2003,6,30]],"date-time":"2003-06-30T18:58:58Z","timestamp":1056999538000},"page":"303-318","source":"Crossref","is-referenced-by-count":14,"title":["A geometric approach to feedback stabilization of nonlinear systems with drift"],"prefix":"10.1016","volume":"50","author":[{"given":"Hannah","family":"Michalska","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel","family":"Torres-Torriti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"11","key":"10.1016\/S0167-6911(03)00169-5_BIB1","doi-asserted-by":"crossref","first-page":"1746","DOI":"10.1109\/9.173144","article-title":"Control and stabilization of nonholonomic dynamic systems","volume":"37","author":"Bloch","year":"1992","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB2","series-title":"Differential Geometric Control Theory","first-page":"181","article-title":"Asymptotic stability and feedback stabilization","author":"Brockett","year":"1983"},{"issue":"8","key":"10.1016\/S0167-6911(03)00169-5_BIB3","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.1109\/9.871753","article-title":"Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups","volume":"45","author":"Bullo","year":"2000","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB4","series-title":"Control System Applications","first-page":"1303","article-title":"Spacecraft attitude control","author":"Coppola","year":"2000"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB5","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/BF01211563","article-title":"Global asymptotic stabilization for controllable systems without drift","volume":"5","author":"Coron","year":"1992","journal-title":"Math. Control Signals Systems"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB6","unstructured":"J.-M. Coron, J.-B. Pomet, A remark on the design of time-varying stabilizing feedback laws for controllable systems without drift, Nonlinear Control Systems Design Symposium \u201992 (NOLCOS92), Bordeaux, France, 24\u201326 June 1992, pp. 413\u2013417."},{"issue":"4","key":"10.1016\/S0167-6911(03)00169-5_BIB7","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1109\/TAC.1984.1103519","article-title":"Spacecraft attitude control and stabilization","volume":"AC-29","author":"Crouch","year":"1984","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB8","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/BF02095991","article-title":"R\u00e9alisation locale des syst\u00e8mes non lin\u00e9aires, alg\u00e8bres de Lie filtr\u00e9es transitives et s\u00e9ries g\u00e9n\u00e9ratrices non commutatives","volume":"71","author":"Fliess","year":"1983","journal-title":"Invent. Math."},{"issue":"5","key":"10.1016\/S0167-6911(03)00169-5_BIB9","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/S0005-1098(98)00211-8","article-title":"Steering of a class of nonholonomic systems with drift terms","volume":"35","author":"Godhavn","year":"1999","journal-title":"Automatica J. IFAC"},{"issue":"4","key":"10.1016\/S0167-6911(03)00169-5_BIB10","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1137\/0318027","article-title":"On the synthesis of a stabilizing feedback control via Lie algebraic methods","volume":"18","author":"Hermes","year":"1980","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"10.1016\/S0167-6911(03)00169-5_BIB11","first-page":"238","article-title":"Nilpotent and high-order approximations of vector field systems","volume":"33","author":"Hermes","year":"1991","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/S0167-6911(03)00169-5_BIB12","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/0022-0396(75)90017-0","article-title":"Controllability in nonlinear systems","volume":"19","author":"Hirschorn","year":"1975","journal-title":"J. Differential Equations"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB13","doi-asserted-by":"crossref","unstructured":"I.V. Kolmanovsky, N.H. McClamroch, V.T. Coppola, Controllability of a class of nonlinear systems with drift, in: Proceedings of the 33rd Conference on Decision & Control, Lake Buena Vista, FL, USA, December 1994, pp. 1254\u20131255.","DOI":"10.1109\/CDC.1994.411153"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB14","series-title":"Nonholonomic Motion Planning","first-page":"235","article-title":"A differential geometric approach to motion planning","author":"Lafferriere","year":"1993"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB15","unstructured":"N.E. Leonard, P.S. Krishnaprasad, Averaging on Lie groups, attitude, control and drift, in: Proceedings of the Twenty-Seventh Annual Conference on Information Sciences and Systems, The Johns Hopkins University, March 1993, pp. 369\u2013374."},{"key":"10.1016\/S0167-6911(03)00169-5_BIB16","doi-asserted-by":"crossref","unstructured":"W. Magnus, On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math. VII (1954) 649\u2013673.","DOI":"10.1002\/cpa.3160070404"},{"issue":"5","key":"10.1016\/S0167-6911(03)00169-5_BIB17","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/002071798221605","article-title":"Time-varying homogeneous feedback","volume":"71","author":"M'Closkey","year":"1998","journal-title":"Internat. J. Control"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB18","doi-asserted-by":"crossref","unstructured":"H. Michalska, F.U. Rehman, Time-varying feedback synthesis for a class of nonhomogeneous systems, in: Proceedings of the 36th Conference on Decision & Control, San Diego, CA, USA, December 1997, pp. 4018\u20134021.","DOI":"10.1109\/CDC.1997.652494"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB19","doi-asserted-by":"crossref","unstructured":"H. Michalska, M. Torres-Torriti, Time-varying stabilizing feedback control for nonlinear systems with drift, in: Proceedings of the 40th Conference on Decision and Control, Vol. 2, Orlando, FL, U.S.A., December 2001, pp. 1767\u20131768.","DOI":"10.1109\/CDC.2001.981159"},{"issue":"4","key":"10.1016\/S0167-6911(03)00169-5_BIB20","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1109\/9.566663","article-title":"Time-varying exponential stabilization of a rigid spacecraft with two control torques","volume":"42","author":"Morin","year":"1997","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB21","doi-asserted-by":"crossref","unstructured":"R. Palais, Global Formulation of the Lie Theory of Transformation Groups, Mem. Amer. Math. Soc., Vol. 22, AMS, Providence, RI, 1957.","DOI":"10.1090\/memo\/0022"},{"issue":"1","key":"10.1016\/S0167-6911(03)00169-5_BIB22","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/9.739086","article-title":"Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle","volume":"AC-44","author":"Pettersen","year":"1999","journal-title":"IEEE Trans. Automat. Control"},{"issue":"9","key":"10.1016\/S0167-6911(03)00169-5_BIB23","doi-asserted-by":"crossref","first-page":"1663","DOI":"10.1109\/9.788533","article-title":"Dynamics and control of a class of underactuated mechanical systems","volume":"44","author":"Reyhanoglu","year":"1999","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB24","series-title":"Lie Algebras and Lie Groups","author":"Serre","year":"1965"},{"issue":"5","key":"10.1016\/S0167-6911(03)00169-5_BIB25","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1137\/0321042","article-title":"Lie brackets and local controllability","volume":"21","author":"Sussmann","year":"1983","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/S0167-6911(03)00169-5_BIB26","unstructured":"H.J. Sussmann, A product expansion for the Chen series, in: C.I. Byrnes, A. Lindquist (Eds.), Theory and Applications of Nonlinear Control Systems, North-Holland, Amsterdam, 1986, pp. 323\u2013335."},{"issue":"1","key":"10.1016\/S0167-6911(03)00169-5_BIB27","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1137\/0325011","article-title":"A general theorem on local controllability","volume":"25","author":"Sussmann","year":"1987","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/S0167-6911(03)00169-5_BIB28","doi-asserted-by":"crossref","unstructured":"M. Torres-Torriti, H. Michalska, A software package for Lie algebraic computations, SIAM Rev., submitted.","DOI":"10.1137\/S0036144502410427"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB29","series-title":"Lie Groups, Lie Algebras, and their Representations","author":"Varadarajan","year":"1984"},{"key":"10.1016\/S0167-6911(03)00169-5_BIB30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1090\/S0002-9939-1964-0160009-0","article-title":"On global representations of the solutions of linear differential equations as products of exponentials","volume":"15","author":"Wei","year":"1964","journal-title":"Proc. Amer. Math. Soc"}],"container-title":["Systems & Control Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167691103001695?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0167691103001695?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T16:17:25Z","timestamp":1585066645000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0167691103001695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,11]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2003,11]]}},"alternative-id":["S0167691103001695"],"URL":"https:\/\/doi.org\/10.1016\/s0167-6911(03)00169-5","relation":{},"ISSN":["0167-6911"],"issn-type":[{"value":"0167-6911","type":"print"}],"subject":[],"published":{"date-parts":[[2003,11]]}}}