InforLorV4, Hal, Corpus, bibRecord, 001B07

Deciding stability and mortality of piecewise affine dynamical systems

Identifieur interne : 001B07 ( Hal/Corpus ); précédent : 001B06; suivant : 001B08

Deciding stability and mortality of piecewise affine dynamical systems

Auteurs : Vincent D. Blondel ; Olivier Bournez ; Pascal Koiran ; Christos Papadimitriou ; John N. Tsitsiklis

Source :

Theoretical Computer Science [ 0304-3975 ] ; 2001.

RBID : Hal:inria-00100820

Abstract

We show that several global properties (attractivity, global asymptotic stability and mortality) of discrete time dynamical systems defined by iteration of piecewise-affine maps are undecidable. Such results had been known only for local properties (e.g., point-to-point reachability). These three properties are undecidable in dimension at least two, but turn out to be decidable in one dimension for continuous maps. This gives a partial answer to a question of Sontag on the decidability of the stability of saturated linear dynamical systems.

Url:

https://hal.inria.fr/inria-00100820

Links to Exploration step

Hal:inria-00100820

Le document en format XML

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<front><div type="abstract" xml:lang="en">We show that several global properties (attractivity, global asymptotic stability and mortality) of discrete time dynamical systems defined by iteration of piecewise-affine maps are undecidable. Such results had been known only for local properties (e.g., point-to-point reachability). These three properties are undecidable in dimension at least two, but turn out to be decidable in one dimension for continuous maps. This gives a partial answer to a question of Sontag on the decidability of the stability of saturated linear dynamical systems.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Deciding stability and mortality of piecewise affine dynamical systems</title>
<author role="aut"><persName><forename type="first">Vincent D.</forename>
<surname>Blondel</surname>
</persName>
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<author role="aut"><persName><forename type="first">Olivier</forename>
<surname>Bournez</surname>
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<email>Olivier.Bournez@loria.fr</email>
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<surname>Papadimitriou</surname>
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<idno type="halAuthorId">132044</idno>
<orgName ref="#struct-365189"></orgName>
<affiliation ref="#struct-805"></affiliation>
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<author role="aut"><persName><forename type="first">John N.</forename>
<surname>Tsitsiklis</surname>
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<idno type="issn">0304-3975</idno>
<title level="j">Theoretical Computer Science</title>
<imprint><publisher>Elsevier</publisher>
<biblScope unit="volume">255</biblScope>
<biblScope unit="issue">1-2</biblScope>
<biblScope unit="pp">687-696</biblScope>
<date type="datePub">2001</date>
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<textClass><keywords scheme="author"><term xml:lang="it">stabilit</term>
<term xml:lang="it">computability</term>
<term xml:lang="it">stability</term>
<term xml:lang="it">calculabilité</term>
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<abstract xml:lang="en">We show that several global properties (attractivity, global asymptotic stability and mortality) of discrete time dynamical systems defined by iteration of piecewise-affine maps are undecidable. Such results had been known only for local properties (e.g., point-to-point reachability). These three properties are undecidable in dimension at least two, but turn out to be decidable in one dimension for continuous maps. This gives a partial answer to a question of Sontag on the decidability of the stability of saturated linear dynamical systems.</abstract>
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Deciding stability and mortality of piecewise affine dynamical systems

Deciding stability and mortality of piecewise affine dynamical systems

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