The stability of saturated linear dynamical systems is undecidable

Vincent D. Blondel Olivier Bournez 1 Pascal Koiran 2 John N. Tsitsiklis
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 LIP - Laboratoire d'Imagerie Paramétrique
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.
Mots-clés : decidabilité dynamical system computability stability stabilité système dynamique
Type de document :
Communication dans un congrès
Horst Reichel, Sophie Tison. 17th International Symposium on Theoretical Aspects of Computer Science - STACS'2000, 2000, Lille, France, Springer-Verlag, 1770, pp.479-490, 2000, Lecture Notes in Computer Science
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https://hal.inria.fr/inria-00099336
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 08:53:04
Dernière modification le : mercredi 21 mars 2018 - 18:57:11

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  • HAL Id : inria-00099336, version 1

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Vincent D. Blondel, Olivier Bournez, Pascal Koiran, John N. Tsitsiklis. The stability of saturated linear dynamical systems is undecidable. Horst Reichel, Sophie Tison. 17th International Symposium on Theoretical Aspects of Computer Science - STACS'2000, 2000, Lille, France, Springer-Verlag, 1770, pp.479-490, 2000, Lecture Notes in Computer Science. 〈inria-00099336〉

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