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Feedback transformations on tori

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Abstract

Here we investigate the problem of transforming a nonlinear system on the torusT n by using global feedback and global changes of coordinates into an invariant system (i.e., a control system\(\dot x = f(x) + \sum\nolimits_{i = 1}^m {g_i (x)u_i }\) of whichf andg i are (left and right) invariant vector fields whenT 2 is considered as a Lie group). We provide a complete answer whenn=2 and give a sufficient condition and necessary conditions in the more general case.

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References

  1. A. Denjoy, Sur les courbes defines par les équations différentielles á la surface du tore,J. Math. Pures Appl.,11 (1983), 333–375.

    Google Scholar 

  2. G. Hector and U. Hirsh,Introduction to the Geometry of Foliations, Part A, Vieweg and Soh, Viesbaden, 1981.

    Google Scholar 

  3. M. R. Herman,Sur la congugaison differentiable des diffeomorphisms du cercle a des rotation, IHES Publ. Math. No. 49, 1979, pp. 5–234.

  4. C. L. Siegel, Notes on differential equations on the torus,Ann. of Math.,46 (1945), 423–428.

    Google Scholar 

  5. S. Sternber,Cellestial Mechanics, Part II, Benjamin, NY, 1969.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Texas Tech University, 79409, Lubbock, TX, USA

    Wijesuriya Dayawansa & Clyde Martin

  2. Department of Systems Science and Mathematics, Washington University, 63130, St. Louis, MO, USA

    David Elliott

Authors
  1. Wijesuriya Dayawansa
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  2. David Elliott
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  3. Clyde Martin
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Dayawansa, W., Elliott, D. & Martin, C. Feedback transformations on tori. Math. Systems Theory 22, 213–219 (1989). https://doi.org/10.1007/BF02088298

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  • DOI: https://doi.org/10.1007/BF02088298

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