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1995 | 32 | 1 | 19-33
Tytuł artykułu

Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We define, in an infinite-dimensional differential geometric framework, the 'infinitesimal Brunovský form' which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by 'endogenous dynamic feedback'.
Rocznik
Tom
32
Numer
1
Strony
19-33
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Secc. de Control Automático, Dep. de Ingen. Elétrica, CINVESTAV - IPN, Ap. Postal 14-740, 07000 México, D.F., Mexico
autor
  • Laboratoire d'Automatique de Nantes, U.R.A. C.N.R.S. 823, E. C. N., 1 Rue de la Noë, 44072 Nantes Cédex, France
autor
  • I.N.R.I.A., 2004 Route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cédex, France
Bibliografia
  • [1] E. Aranda, C. H. Moog and J.-B. Pomet, A linear algebraic framework for dynamic feedback linearization, IEEE Trans. Automatic Control, 40 (1995), 127-132.
  • [2] E. Aranda, C. H. Moog and J.-B. Pomet, Feedback linearization: a linear algebraic approach, in: 22nd IEEE Conf. on Dec. and Cont., Dec. 1993.
  • [3] P. Brunovský, A classification of linear controllable systems, Kybernetika 6 (1970), 176-188.
  • [4] B. Charlet, J. Lévine and R. Marino, On dynamic feedback linearization, Syst. & Contr. Lett. 13 (1989), 143-151.
  • [5] B. Charlet, J. Lévine and R. Marino, Sufficient conditions for dynamic feedback linearization, SIAM J. Contr. Opt. 29 (1991), 38-57.
  • [6] J.-M. Coron, Linearized control systems and applications to smooth stabilization, SIAM J. Contr. Opt. 32 (1994), 358-386.
  • [7] M. D. Di Benedetto, J. Grizzle and C. H. Moog, Rank invariants of nonlinear systems, SIAM J. Contr. Opt. 27 (1989), 658-672.
  • [8] M. Fliess, Automatique et corps différentiels, Forum Math. 1 (1989), 227-238.
  • [9] M. Fliess, Some remarks on the Brunovský canonical form, preprint, L.S.S., Ec. Sup. d'Elec., Gif-sur-Yvette, France, 1992, to appear in Kybernetika.
  • [10] M. Fliess and S. T. Glad, An algebraic approach to linear and nonlinear control, in: H. L. Trentelman and J. C. Willems (eds.), Essays on Control: Perspectives in the Theory and its Applications, PSCT 14, Birkhäuser, Boston, 1993.
  • [11] M. Fliess, J. Lévine, P. Martin and P. Rouchon, On differentially flat nonlinear systems, in: 2nd. IFAC NOLCOS Symposium, 1992, 408-412.
  • [12] M. Fliess, J. Lévine, P. Martin and P. Rouchon, Sur les systèmes non linéaires différentiellement plats, C. R. Acad. Sc. Paris, 315-I (1992), 619-624.
  • [13] A. Ilchmann, I. Nürnberger and W. Schmale, Time-varying polynomial matrix systems, Int. J. Control 40 (1984), 329-362.
  • [14] B. Jakubczyk, Remarks on equivalence and linearization of nonlinear systems, in: 2nd. IFAC NOLCOS Symposium, 1992, 393-397.
  • [15] B. Jakubczyk, Dynamic feedback equivalence of nonlinear control systems, preprint, 1993.
  • [16] P. Martin, Contribution à l'étude des systèmes non linéaires différentiellement plats, Thèse de Doctorat, Ecole des Mines de Paris, 1992.
  • [17] P. Martin, A geometric sufficient conditions for flatness of systems with m inputs and m+1 states, in: 22nd IEEE Conf. on Dec. and Cont., Dec. 1993, 3431-3435.
  • [18] P. Martin, A criterion for flatness with structure {1,...,1,2}, preprint, 1992.
  • [19] P. Martin and P. Rouchon, Systems without drift and flatness, in: Int. Symp. on Math. Theory on Networks and Syst., Regensburg, August 1993.
  • [20] J.-B. Pomet, On dynamic feedback linearization of four-dimensional affine control systems with two inputs, preprint, 1993, INRIA report No 2314.
  • [21] J.-B. Pomet, A differential geometric setting for dynamic equivalence and dynamic linearization, this volume, 319-339.
  • [22] J.-B. Pomet, C. H. Moog and E. Aranda, A non-exact Brunovský form and dynamic feedback linearization, in: Proc. 31st. IEEE Conf. Dec. Cont., 1992, 2012-2017.
  • [23] E. D. Sontag, Finite-dimensional open-loop control generators for nonlinear systems, Int. J. Control 47 (1988), 537-556.
  • [24] H. J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems, J. Diff. Eq. 12 (1972), 95-116.
  • [25] W. A. Wolovich, Linear Multivariable Systems, Applied Math. Sci. 11, Springer, 1974.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv32z1p19bwm
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