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The Stability of Saturated Linear Dynamical Systems Is Undecidable

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only for point-to-point properties. We prove these properties undecidable for saturated linear dynamical systems, and for continuous piecewise affine dynamical systems in dimension three. We also describe some consequences of our results on the possible dynamics of such systems.

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Author information

Authors and Affiliations

  1. Department of Mathematical Engineering, Université catholique de Louvain, Avenue Georges Lemaitre 4, B-1348, Louvain-la-Neuve, Belgium

    Vincent D. Blondel

  2. LORIA, Campus Scientifique BP 239, 54506, Vandoeuvre-les-Nancy, France

    Olivier Bournez

  3. LIP, ENS Lyon, 46 allée d’Italie, F-69364, Lyon Cedex 07, France

    Pascal Koiran

  4. LIDS, MIT, Cambridge, MA, 02139, USA

    John N. Tsitsiklis

Authors
  1. Vincent D. Blondel
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  2. Olivier Bournez
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  3. Pascal Koiran
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  4. John N. Tsitsiklis
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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© 2000 Springer-Verlag Berlin Heidelberg

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Blondel, V.D., Bournez, O., Koiran, P., Tsitsiklis, J.N. (2000). The Stability of Saturated Linear Dynamical Systems Is Undecidable. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_40

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  • DOI: https://doi.org/10.1007/3-540-46541-3_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

  • eBook Packages: Springer Book Archive

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