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Some remarks on nonlinear input-output systems with delays

  • II-Algebraic System Theory
  • Conference paper
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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

We outline a general theory of nonlinear input-output differential systems with delays by employing difference-differential algebra.

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References

  1. Bialynicki-Birula, A., On Galois theory of fields with operators, Amer. J. Math., 84, 1962, 89–109.

    Google Scholar 

  2. N. Bourbaki, Algèbre, chap.4 to 7, Masson, Paris, 1981.

    Google Scholar 

  3. Brewer, J.W., Bunce, J.W., and Van Vleck, F.S., Linear Systems over Commutative Rings, Marcel Dekker, New York, 1986.

    Google Scholar 

  4. Byrnes, C.I., On the control of certain deterministic infinite-dimensional systems by algebro-geometric techniques, Amer. J. Math., 100, 1978, 1333–1381.

    Google Scholar 

  5. Cohn, R.M., Difference Algebra, Interscience, New York, 1965.

    Google Scholar 

  6. Cohn, R.M., A difference-differential basis theorem, Canad. J. Math., 22, 1970, 1224–1237.

    Google Scholar 

  7. Datta, K.B., and Hautus, M.L.J., Decoupling of multivariable control systems over unique factorization domains, SIAM J. Control Optimiz., 22, 1984, 28–39.

    Google Scholar 

  8. Fliess, M., Esquisses pour une théorie des systèmes non linéaires en temps discret, Proc. Conf. Linear Nonlinear Math. Control Theory, Torino, July 1986, Rend. Semin. Mat. Univ. Politec. Torino, Fasc. spec. 1987, pp.55–67.

    Google Scholar 

  9. Fliess, M., Automatique et corps différentiels, Forum Math., 1, 1989.

    Google Scholar 

  10. Fliess, M., Automatique en temps discret et algèbre aux différences, to appear.

    Google Scholar 

  11. Kamen, E.W., On an algebraic theory of systems defined by convolution operators, Math. Systems Theory, 9, 1975, 57–74.

    Google Scholar 

  12. Kaplansky, I., An Introduction to Differential Algebra, Hermann, Paris, 1957.

    Google Scholar 

  13. Kolchin, E.R., Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.

    Google Scholar 

  14. Ritt, J.F., Differential Algebra, Amer. Math. Soc., New York, 1950.

    Google Scholar 

  15. Rouchaleau, Y., and Wyman, B., Linear dynamical systems over integral domains, J. Comput. Systems Sci., 9, 1974, 129–142.

    Google Scholar 

  16. Rouchaleau, Y., Wyman, B., and Kalman, R.E., Algebraic structure of linear dynamical systems III: Realization theory over a commutative ring, Proc. Nat. Acad. Sci. USA, 69, 1972, 3404–3406.

    Google Scholar 

  17. Sontag, E.D., Linear systems over commutative rings: A survey, Ricerche Automatica, 7, 1976, 1–33.

    Google Scholar 

  18. Willems, J.C., From time series to linear systems, I: Finite dimensional linear time invariant systems, Automatica, 22, 1986, 561–580.

    Google Scholar 

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Authors

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J. Descusse Michel Fliess A. Isidori D. Leborgne

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© 1989 Springer-Verlag

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Fliess, M. (1989). Some remarks on nonlinear input-output systems with delays. 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/BFb0043026

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  • DOI: https://doi.org/10.1007/BFb0043026

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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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