Genericity of observability of control-affine systems

M. Balde; P. Jouan

ESAIM: Control, Optimisation and Calculus of Variations (1998)

  • Volume: 3, page 345-359
  • ISSN: 1292-8119

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Balde, M., and Jouan, P.. "Genericity of observability of control-affine systems." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 345-359. <http://eudml.org/doc/90529>.

@article{Balde1998,
author = {Balde, M., Jouan, P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {smooth control systems; genericity; differential observability; affine systems; transversality},
language = {eng},
pages = {345-359},
publisher = {EDP Sciences},
title = {Genericity of observability of control-affine systems},
url = {http://eudml.org/doc/90529},
volume = {3},
year = {1998},
}

TY - JOUR
AU - Balde, M.
AU - Jouan, P.
TI - Genericity of observability of control-affine systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 345
EP - 359
LA - eng
KW - smooth control systems; genericity; differential observability; affine systems; transversality
UR - http://eudml.org/doc/90529
ER -

References

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  1. [1] R. Abraham, J. Robbin: Tranversal mappings and flows, W.A. Benjamin, Inc., 1967. Zbl0171.44404MR240836
  2. [2] D. Aeyels: Generic observability of differentiable systems, SIAM J. Contr. Opt., 19, 1981, 595-603. Zbl0474.93016MR626654
  3. [3] D. Aeyels: Global observability of Morse-Smale systems, J. Diff. Equations, 45, 1982, 1-15. Zbl0454.58010MR662483
  4. [4] J. Bochnak, M. Coste, M-F. Roy: Géométrie algébrique réelle, Ergebnisse der Mathematik, Springer-Verlag, 1987. Zbl0633.14016MR949442
  5. [5] J.-P. Gauthier, H. Hammouri, I. Kupka: Observers for non-linear systems, IEEE CDC Conference, december 1991, 1483-1489. 
  6. [6] J.-P. Gauthier, I. Kupka: Observability and observers for nonlinear systems, SIAM J. Contr. Opt., 32, 4, 1994, 975-994. Zbl0802.93008MR1280224
  7. [7] J.-P. Gauthier, I. Kupka: Observability for systems with more outputs than inputs and asymptotic observers, Math. Z. 223, 1996, 47-78. Zbl0863.93008MR1408862
  8. [8] J.-P. Gauthier, I. Kupka: Genericity of observability and the existence of nonlinear observers, Banach Center publications, 32, Warszawa 1995, 227-244. Zbl0839.93020MR1364431
  9. [9] M. Golubitsky, V. Guillemin: Stable mappings and their singularities, Graduate texts in mathematics, Springer-Verlag, 1973. Zbl0294.58004MR341518
  10. [10] R. Hermann, J. Krener: Nonlinear controlability and observability, IEEE Trans. Automat. Contr., AC-22, 1977, 728-740. Zbl0396.93015MR476017
  11. [11] H. Hironaka: Subanalytic sets, in Number theory, Algebraic geometry and Commutative algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo, 1973, 453-493. Zbl0297.32008MR377101
  12. [12] M.W. Hirsch: Differential topology, Graduate texts in mathematics, Springer-Verlag, 1976. Zbl0356.57001MR448362
  13. [13] Ph. Jouan: Observability of real analytic vector-fields on compact manifolds, Systems Control Lett., 26, 2, Septembre 1995. Zbl0877.93011MR1349539
  14. [14] Ph. Jouan: Contribution à l'étude de la généricité de l'observabilité des systèmes contrôlés, submitted to C. R. Acad. Sci. Paris. 
  15. [15] Ph. Jouan: Singularités des systèmes non linéaires. Observabilité et observateurs, Thèse de l'Université de Rouen, 1995. 
  16. [16] Ph. Jouan, J.-P. Gauthier: Finite singularities of nonlinear systems. Output stabilization, observability and observers, Journal of Dynamical and Control Systems, 2, 2, 1996, 255-288. Zbl0944.93026MR1388697
  17. [17] S. Lojasiewicz: Triangulation of semi analytic sets, Annal. Sc. Nor. Sup. PISA, 1966, 449-474. Zbl0128.17101MR173265
  18. [18] H.J. Sussmann: Single-input observability of continuous-time systems, Math. Syst. Theory, 12, 1979, 371-393. Zbl0422.93019MR541865
  19. [19] F. Takens: Detecting strange attractors in turbulence, in Dynamic Systems and Turbulence, Warwick, 1980, Springer-Verlag, Berlin, 1981, 366-381. Zbl0513.58032MR654900
  20. [20] K. Tchon: On solvability of several affine system problems, Systems Contr. Lett., 4, 1984, 373-379. Zbl0544.93031MR768563

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