Global Feedback Linearizability of Locally Linearizable Systems

  • William M. Boothby
Part of the Mathematics and Its Applications book series (MAIA, volume 29)


This paper is dedicated to Wilfred Kaplan and to Georges Reeb as a token of my admiration and friendship.


Vector Field Integral Curve Equivalent System Curve Family Complex Analytic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    W.M. Boothby, Some comments on global linearization of nonlinear systems, Systems and Control Letters, 4 (1983), 143–147.MathSciNetCrossRefGoogle Scholar
  2. [2]
    C.I. Byrnes, Remarks on nonlinear planar control systems which are linearized by feedback, preprint.Google Scholar
  3. [3]
    D. Cheng, T.J. Tarn and A. Isidori, Global feedback linearization of nonlinear systems, Proc. 23nd Conf. on Decision & Control, Las Vegas, NV, Dec. 1984.Google Scholar
  4. [4]
    D. Cheng, T.J. Tarn and A. Isidori, Global external linarization of nonlinear systems via feedback, Proc. 23nd Conf. on Decision & Control, Las Vegas NV, Dec. 1984.Google Scholar
  5. [5]
    L. Conlon, Transversally parallelizable foliations of codimension two, Trans. Amer. Math. Soc., 194 (1974), 79–102, also Erratum, loc. cit. 207 (1975), 406.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    L.R. Hunt, R. Su and G. Meyer, Global transformations of nonlinear systems, To appear in IEEE Trans, on Autom. Control, Vol. 27 (1982).Google Scholar
  7. [7]
    B. Jakubczyk and W. Respondek, On linearization of control systems, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys., 28 (1980), 517–522.MathSciNetzbMATHGoogle Scholar
  8. [8]
    W. Kaplan, Regular curve families filling the plane I, Duke Math J., 7 (1940), 154–185.MathSciNetCrossRefGoogle Scholar
  9. [9]
    W. Kaplan, Regular curve families filling the plane II, Duke Math J., 8 (1941), 11–45.MathSciNetCrossRefGoogle Scholar
  10. [10]
    W. Kaplan, Topology of the level curves of harmonic functions, Trans. Am. Math. Soc. 63 (1948), 514–522.zbMATHCrossRefGoogle Scholar
  11. [11]
    L. Markus, Parallel dynamical systems, Topology 8 (1969), 47–57.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    G. Reeb, Sur certaines proprietes topologique des varietes feuilletes, Actualites Sci Industr. no. 1183, Hermann, Paris 1952.Google Scholar
  13. [13]
    R. Su, On the linear equivalents of nonlinear systems, Systems and Control Letters 2, No. 1 (1982).Google Scholar
  14. [14]
    T. Wazewski, Sur un probleme de caractere integral relatif a l’equation \( \frac{{\partial z}}{{\partial x}} + (\alpha (x,y)\frac{{\partial z}}{{\partial y}} = 0) \), Mathematica Cluj, 8 (1934), 103–116.zbMATHGoogle Scholar
  15. [15]
    A. Haefliger, Varietes feuilletees, Ann. Scuola Norm. Sup. Pisa (3) 16 (1962), 367–379.MathSciNetzbMATHGoogle Scholar
  16. [16]
    A. Haefliger and G. Reeb, Varietes (non separees) a une dimension et structures feuillettees du plan, L’Enseignement Math., 3 (1957), 107–125.MathSciNetzbMATHGoogle Scholar
  17. [17]
    W. Dayawansa, W.M. Boothby and D.L. Elliott, Global state and feedback equivalence of nonlinear systems, to appear, Systems and Control Letters.Google Scholar
  18. [18]
    W. Dayawansa, D.L. Elliott and W.M. Boothby, Global linearization by feedback and state transformations. To appear, IEEE Conference on Decision and Control, December 1985.Google Scholar
  19. [19]
    W. Dayawansa, Ph.D. Dissertation, Washington University, 1985.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • William M. Boothby
    • 1
  1. 1.Department of MathematicsWashington UniversitySt. LouisUSA

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