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The stability of saturated linear dynamical systems is undecidable

Identifieur interne : 009B19 ( Main/Merge ); précédent : 009B18; suivant : 009B20

The stability of saturated linear dynamical systems is undecidable

Auteurs : Vincent D. Blondel ; Olivier Bournez [France] ; Pascal Koiran [France] ; John N. Tsitsiklis

Source :

Journal of Computer and System Sciences [ 0022-0000 ] ; 2001.

RBID : Hal:inria-00100924

English descriptors

mix :
- computability, dynamical systems, décidabilite, stabilite, stability, systèmes dynamiques.

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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https://hal.inria.fr/inria-00100924

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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The stability of saturated linear dynamical systems is undecidable

The stability of saturated linear dynamical systems is undecidable

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

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