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Regularly persistent observers for bilinear systems

  • I-Differential Geometric System Theory Observers
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New Trends in Nonlinear Control Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 122))

Abstract

This paper deals with the problem of synthesis of observers for bilinear systems working for the class of regularly persistent inputs. Moreover we show how this result is related to the Kalman observer for time-varying linear systems.

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References

  1. B.D. ANDERSON, J. MOORE: Linear optimal control, Prentice Hall Network series, 1971.

    Google Scholar 

  2. D. BESTLE-M. ZEITZ: Canonical form design for nonlinear observers with linearizable error dynamics, Internat. J. Control, 198, 23, p.419–431.

    Google Scholar 

  3. G. BORNARD, N. COUENNE, F. CELLE: Proceedings of the International Conference "Automatique Non linéaire", Nantes, June 1988, France.

    Google Scholar 

  4. F. CELLE, J.P. GAUTHIER, D. KASAKOS, G. SALLET: Synthesis of nonlinear observers: a harmonic analysis approach, submitted to MCSS.

    Google Scholar 

  5. Y. FUNAHASHI: Stable state estimator for bilinear systems, Internat. J. Control, 1979, 29, p.181–188.

    Google Scholar 

  6. J.P. GAUTHIER, G. BORNARD: Observability for any u(t) of a class of bilinear systems, IEEE Trans. Automat. Control, 1981, AC 26, p.922–926.

    Google Scholar 

  7. J.P.GAUTHIER, F. CELLE: Theory of dynamic observers for a class of nonlinear systems, MTNS, Janvier 1987, Phoenix.

    Google Scholar 

  8. J.P. GAUTHIER, D. KAZAKOS: Observabilité et observateurs de systèmes non linéaires, RAIRO APII 21, 1987.

    Google Scholar 

  9. O. GRASSELI, A. ISIDORI: Deterministic reconstruction and reachability of bilinear control processes, Roc. JACC, San Francisco, June 22–25, 1977.

    Google Scholar 

  10. O. GRASSELI, A. ISIDORI: An existence theorem for observers of bilinear systems, IEEE Trans. Automat. Control, AC 26, 1981, p.1299–1301.

    Google Scholar 

  11. S. HARA and K. FURUTA: Minimal order state observers for bilinear systems, Internat. J. Control 24, 1976, p.705–718.

    Google Scholar 

  12. R. KALMAN: Contributions to the theory of optimal control, Proceedings of the Conference on Differential Equations, Mexico City, Mexico, 1959; Bol. Soc. Mat. Mex. 1961.

    Google Scholar 

  13. R. KALMAN, R. BUCY: New results in linear filtering and prediction theory, J. of Basic Engineering 82 D (1960) 35–45.

    Google Scholar 

  14. R. KALMAN, P. FALB, M. ARBIB: Topics in mathematical systems theory, Mac Graw Hill, 1969.

    Google Scholar 

  15. S.R. KOU, D.L. ELLIOT, T.J. TARN: Exponential observers for nonlinear dynamics systems, Inform. and Control 29, 1975, p.204–216.

    Google Scholar 

  16. A.J. KRENER, A. ISIDORI: Linearization by output injection and nonlinear dynamics systems, Systems Control Lett. 3, 1983, p.47–52.

    Google Scholar 

  17. A.J. KRENER, W. RESPONDEK: Nonlinear observers with linear error dynamics, SIAM J. Control Optim. 23, 1985, p.197–216.

    Google Scholar 

  18. M. KWAKERNAAK: Linear optimal control theory, New York, J. Wiley cop. 1972.

    Google Scholar 

  19. J. LEVINE, R. MARINO: Nonlinear system immersion, observers and finite dimensional filters, Systems and Control Letters, 7, 1986, p.137–142.

    Google Scholar 

  20. E. SONTAG: On the observability of polynomial systems, SIAM J. on Control and Optimization 17, 1979.

    Google Scholar 

  21. E. SONTAG: Nonlinear regulation: the piecewise linear approach, IEEE Trans. on Aut. Control, vol. AC 26, no 2, April 1981.

    Google Scholar 

  22. H. J. SUSSMANN: Single input observability of continuous time systems, Math. Systems Theory 12, 1979, p.371–393.

    Google Scholar 

  23. D. WILLIAMSON: Observability of bilinear systems, with applications to biological control, Automatica 13, 1977, p.243–254.

    Google Scholar 

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J. Descusse Michel Fliess A. Isidori D. Leborgne

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© 1989 Springer-Verlag

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Bornard, G., Couenne, N., Celle, F. (1989). Regularly persistent observers for bilinear systems. In: Descusse, J., Fliess, M., Isidori, A., Leborgne, D. (eds) New Trends in Nonlinear Control Theory. Lecture Notes in Control and Information Sciences, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043023

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  • DOI: https://doi.org/10.1007/BFb0043023

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51075-8

  • Online ISBN: 978-3-540-46143-2

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