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Manifolds, Vectorfields, Lie Brackets, Distributions

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Nonlinear Dynamical Control Systems

Abstract

In the previous chapter we have seen that many nonlinear control systems.

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References

  1. R.A. Abraham and J.E. Marsden. Foundations of Mechanics. Benjamin/Cummings, Reading, 1978.

    Google Scholar 

  2. T. Bröcker and K. Jänich. Einführung in die Differentialtopologie. Springer, Berlin, 1973.

    Google Scholar 

  3. W.A. Boothby. An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, New York, 1975.

    Google Scholar 

  4. R. Hermann. The differential geometry of foliations. J. Math. and Mech., 11:302–306, 1962.

    Google Scholar 

  5. A. Isidori. Nonlinear Control Systems: An Introduction, volume 72 of Lect. Notes Contr. Inf. Sci. Springer-Verlag, Berlin, 1985.

    Google Scholar 

  6. T. Nagano. Linear differential systems with singularities and applications to transitive Lie algebras. J. Math. Soc. Japan, 18:398–404, 1966.

    Google Scholar 

  7. M. Spivak. A comprehensive introduction to differential geometry, Vol I. Publish or Perish, Boston, 1970.

    Google Scholar 

  8. H. Sussmann. Orbits of families of vectorfields and integrability of distributions. Trans. Amer. Math. Soc., 180:171–188, 1973.

    Google Scholar 

  9. F.W. Warner. Foundations of differentiable manifolds and Lie groups. Scott, Foresman, Glenview, 1970.

    Google Scholar 

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Correspondence to Henk Nijmeijer .

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© 1990 Springer Science+Business Media New York 1990, Corrected printing 2016

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Nijmeijer, H., van der Schaft, A. (1990). Manifolds, Vectorfields, Lie Brackets, Distributions. In: Nonlinear Dynamical Control Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2101-0_2

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  • DOI: https://doi.org/10.1007/978-1-4757-2101-0_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-2102-7

  • Online ISBN: 978-1-4757-2101-0

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