Free Access
Issue
ESAIM: COCV
Volume 13, Number 2, April-June 2007
Page(s) 237 - 264
DOI https://doi.org/10.1051/cocv:2007011
Published online 12 May 2007
  1. E. Aranda-Bricaire, C.H. Moog and J.-B. Pomet, An infinitesimal Brunovsky form for nonlinear systems with applications to dynamic linearization. Banach Center Publications 32 (1995) 19–33. [Google Scholar]
  2. D. Avanessoff, Linéarisation dynamique des systèmes non linéaires et paramétrage de l'ensemble des solutions. Ph.D. thesis, University of Nice-Sophia Antipolis (June 2005). [Google Scholar]
  3. R.L. Bryant, S.S. Chern, R.B. Gardner, H.L. Goldschmitt and P.A. Griffiths, Exterior Differential Systems, Springer-Verlag, M.S.R.I. Publications 18 (1991). [Google Scholar]
  4. É. Cartan, Sur l'intégration de certains systèmes indéterminés d'équations différentielles. J. reine angew. Math. 145 (1915) 86–91. [Google Scholar]
  5. B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization. Syst. Control Lett. 13 (1989) 143–151. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  6. B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic state feedback linearization. SIAM J. Control Optim. 29 (1991) 38–57. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Fliess, J. Lévine, P. Martin and P. Rouchon, Sur les systèmes non linéaires différentiellement plats. C. R. Acad. Sci. Paris Sér. I 315 (1992) 619–624. [Google Scholar]
  8. M. Fliess, J. Lévine, P. Martin and P. Rouchon, Flatness and defect of nonlinear systems: Introductory theory and examples. Int. J. Control 61 (1995) 1327–1361. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Fliess, J. Lévine, P. Martin and P. Rouchon, A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automat. Control 44 (1999) 922–937. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Fliess, J. Lévine, P. Martin and P. Rouchon, Some open questions related to flat nonlinear systems, in Open problems in mathematical systems and control theory, Springer, London (1999) 99–103. [Google Scholar]
  11. M. Golubitsky and V. Guillemin, Stable mappings and their singularities. Springer-Verlag, New York, GTM 14 (1973). [Google Scholar]
  12. D. Hilbert, Über den Begriff der Klasse von Differentialgleichungen. Math. Annalen 73 (1912) 95–108. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Hubert, Notes on triangular sets and triangulation-decomposition algorithms. I: Polynomial systems. II: Differential systems. In F. Winkler et al. eds., Symbolic and Numerical Scientific Computing 2630, 1–87. Lect. Notes Comput. Sci. (2003). [Google Scholar]
  14. A. Isidori, C.H. Moog and A. de Luca, A sufficient condition for full linearization via dynamic state feedback, in Proc. 25th IEEE Conf. on Decision and Control, Athens (1986) 203–207. [Google Scholar]
  15. P. Martin, Contribution à l'étude des systèmes différentiellement plats. Ph.D. thesis, École des Mines, Paris (1992). [Google Scholar]
  16. P. Martin, R.M. Murray and P. Rouchon, Flat systems, in Mathematical control theory, Part 1, 2 (Trieste, 2001), ICTP Lect. Notes VIII, (electronic). Abdus Salam Int. Cent. Theoret. Phys., Trieste (2002) 705–768. [Google Scholar]
  17. P. Martin and P. Rouchon, Feedback linearization and driftless systems. Math. Control Signals Syst. 7 (1994) 235–254. [CrossRef] [MathSciNet] [Google Scholar]
  18. J.-B. Pomet, A differential geometric setting for dynamic equivalence and dynamic linearization. Banach Center Publications 32 (1995) 319–339. [Google Scholar]
  19. J.-B. Pomet, On dynamic feedback linearization of four-dimensional affine control systems with two inputs. ESAIM Control Optim. Calc. Var. 2 (1997) 151–230. http://www.edpsciences.org/cocv/. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  20. J.F. Ritt, Differential Algebra. AMS Coll. Publ. XXXIII. New York (1950). [Google Scholar]
  21. P. Rouchon, Flatness and oscillatory control: some theoretical results and case studies. Tech. report PR412, CAS, École des Mines, Paris (1992). [Google Scholar]
  22. P. Rouchon, Necessary condition and genericity of dynamic feedback linearization. J. Math. Syst. Estim. Contr. 4 (1994) 1–14. [Google Scholar]
  23. W.M. Sluis, A necessary condition for dynamic feedback linearization. Syst. Control Lett. 21 (1993) 277–283. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  24. M. van Nieuwstadt, M. Rathinam and R. Murray, Differential flatness and absolute equivalence of nonlinear control systems. SIAM J. Control Optim. 36 (1998) 1225–1239. http://epubs.siam.org:80/sam-bin/dbq/article/27402. [CrossRef] [MathSciNet] [Google Scholar]
  25. P. Zervos, Le problème de Monge. Mémorial des Sciences Mathématiques, LIII (1932). [Google Scholar]

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