{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:25:32Z","timestamp":1787322332308,"version":"build-2736575974"},"reference-count":33,"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>We consider a class, denoted by ${\\cal Q}$, of the nonlinear control systems which can be densely represented as a subsystem of a certain kind of quadratic system, namely a quadratic target. We say that a system in $\\cal Q$ undergoes a globally exact quadratization. Here \u201cglobally\u201d adds up to a slight extension of the notion of $C^\\infty$ immersion (of systems), namely a dense immersion, which amounts to saying that it is defined on the whole manifold of the system states, except possibly a zero-measure set. It is proven that the class ${\\cal Q}$ includes all systems characterized by vector fields whose components are analytic integral closed-form functions (ICFFs). The result is first proven for algebraic system functions, by means of a constructive proof, and next extended up to analytic ICFFs. For nonanalytic ICFFs a weaker result is proven as well. Also the case of a partially observed system is considered, as well as the internal structure of every quadratic representation, which is proven to be always a feedback interconnection of bilinear systems. Finally, examples are presented for which the constructive proof given earlier is turned into a quadratization algorithm, which can be carried out by hand, and the resulting differential equations of the quadratic representation are presented.<\/jats:p>","DOI":"10.1137\/130915418","type":"journal-article","created":{"date-parts":[[2015,1,20]],"date-time":"2015-01-20T12:21:51Z","timestamp":1421756511000},"page":"235-261","source":"Crossref","is-referenced-by-count":18,"title":["Global Exact Quadratization of Continuous-Time Nonlinear Control Systems"],"prefix":"10.1137","volume":"53","author":[{"given":"Francesco","family":"Carravetta","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,1,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012901391706"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/0321044"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1049"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02212-6"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/0311051"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"A. Isidori,\n                      Nonlinear Control Systems. An Introduction,\n                      Lecture Notes in Control and Inform. Sci. 72, Springer-Verlag, London, UK, 1985.","DOI":"10.1007\/BFb0006368"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"G. Conte, C. H. Moog, and A. M. Perdon,\n                      Algebraic Methods for Nonlinear Control Systems\n                      , 2nd ed., Comm. Control Engrg. Ser., Springer, London, UK, 2007.","DOI":"10.1007\/978-1-84628-595-0"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102604"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(82)80042-X"},{"key":"atypb10","first-page":"1115","author":"Brockett R. W.","year":"1978","journal-title":"Helsinki"},{"key":"atypb11","first-page":"268","author":"Hunt L. R.","year":"1983","journal-title":"Boston"},{"key":"atypb12","first-page":"517","volume":"28","author":"Jakubczyk B.","year":"1980","journal-title":"Bull. Acad. Polon. Sci. Se\u0301r. Sci. Math."},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(83)90037-3"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/0323016"},{"key":"atypb15","first-page":"153","author":"Brockett R. W.","year":"1972","journal-title":"New York"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1973.1100424"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1974.1100617"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/0312040"},{"key":"atypb19","unstructured":"R. R. Mohler,\n                      Bilinear Control Processes\n                      , Academic Press, New York, 1973."},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"P. Pardalos and M. Yatsenko,\n                      Optimization and Control of Bilinear Systems. Theory, Algorithms, and Applications\n                      , Springer Optim. Appl. 11, Springer, New York, 2008.","DOI":"10.1007\/978-0-387-73669-3"},{"key":"atypb21","unstructured":"D. L. Elliot,\n                      Bilinear Control Systems - Matrices in Action\n                      , Springer Applied Mathematical Science 169, Springer-Verlag, New York, 2009."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1985.1103794"},{"key":"atypb23","first-page":"493","volume":"12","author":"Belozyorov V. Y.","year":"2002","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2008.2008528"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1980.1102303"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102742"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1109\/9.536506"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2003.815027"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1137\/0313049"},{"key":"atypb30","first-page":"834","author":"Krener A. J.","year":"1974","journal-title":"Monticello"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/0313053"},{"key":"atypb32","first-page":"80","author":"Carravetta F.","year":"2012","journal-title":"Slovak Republic"},{"key":"atypb33","first-page":"1859","author":"Carravetta F.","year":"2012","journal-title":"HI"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130915418","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:20:46Z","timestamp":1787318446000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130915418"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/130915418"],"URL":"https:\/\/doi.org\/10.1137\/130915418","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}