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Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems

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Algebraic and Geometric Methods in Nonlinear Control Theory

Part of the book series: Mathematics and Its Applications ((MAIA,volume 29))

Abstract

In the last fifteen years a theory for nonlinear control systems has been developed using differential geometric methods. Many problems have been treated in this fashion and interesting results have been obtained for nonlinear equivalence, decomposition, controllability, observability, optimality, synthesis of control (with desired properties: decoupling or noninteracting), linearization and many others. We refer the reader to Sussmann [28] for a survey and bibliography. We want to emphasize only that in most of the papers devoted to nonlinear control systems (using geometric methods) only a local viewpoint is presented. This is due to two kinds of obstructions: singularities of the studied objects (functions, vector fields, distributions) and topological obstructions for the global existence of the sought solutions.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-950, Warsaw, Poland

    Witold Respondek

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  1. Witold Respondek
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Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS — École Supérieure d’Electricité, Gif-sur-Yvette, France

    M. Fliess

  2. Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

    M. Hazewinkel

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© 1986 D. Reidel Publishing Company

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Respondek, W. (1986). Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems. In: Fliess, M., Hazewinkel, M. (eds) Algebraic and Geometric Methods in Nonlinear Control Theory. Mathematics and Its Applications, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4706-1_14

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  • DOI: https://doi.org/10.1007/978-94-009-4706-1_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8593-9

  • Online ISBN: 978-94-009-4706-1

  • eBook Packages: Springer Book Archive

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