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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
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Conference papers
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https://hal.inria.fr/inria-00099336
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:53:04 AM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM

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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. 17th International Symposium on Theoretical Aspects of Computer Science - STACS'2000, LIFL, 2000, Lille, France, pp.479-490. ⟨inria-00099336⟩

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