{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:47:59Z","timestamp":1787320079167,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent, i.e., equivalent via a classical diffeomorphism, or they are both ruled; for systems of different dimensions, the one of higher dimension must be ruled. A ruled system is one whose equations define at each point in the state manifold a ruled submanifold of the tangent space. Dynamic equivalence is also known as equivalence by endogenous dynamic feedback or by a Lie\u2013B\u00e4cklund transformation when control systems are viewed as underdetermined systems of ordinary differential equations; it is very close to absolute equivalence for Pfaffian systems. It was already known that a differentially flat system must be ruled; this was a particular case of the present result, in which one of the systems was assumed to be \u201ctrivial\u201d (or linear controllable).<\/jats:p>","DOI":"10.1137\/080723351","type":"journal-article","created":{"date-parts":[[2009,2,25]],"date-time":"2009-02-25T18:08:43Z","timestamp":1235585323000},"page":"925-940","source":"Crossref","is-referenced-by-count":3,"title":["A Necessary Condition for Dynamic Equivalence"],"prefix":"10.1137","volume":"48","author":[{"given":"Jean-Baptiste","family":"Pomet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,2,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"R. L. Anderson and N. H. Ibragimov,\n                      Lie-B\u00e4cklund Transformations in Applications\n                      , SIAM Stud. Appl. 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Sluis,\n                      Dynamic feedback for classical geometries\n                      , in Differential Geometry and Mathematical Physics (Vancouver, BC, 1993), Contemp. Math. 170, Amer. Math. Soc., Providence, RI, 1994, pp. 207\u2013213.","DOI":"10.1090\/conm\/170\/01755"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(93)90069-I"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(87)90103-4"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"G. R. Wilkens,\n                      Centro-affine geometry in the plane and feedback invariants of two-state scalar control systems\n                      , in Differential Geometry and Control (Boulder, CO, 1997), Proc. Sympos. Pure Math. 64, Amer. Math. 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