Deciding stability and mortality of piecewise affine dynamical systems

Vincent Blondel; Olivier Bournez; Pascal Koiran; Christos Papadimitriou; John Tsitsiklis

Reports

Deciding stability and mortality of piecewise affine dynamical systems

Vincent Blondel ¹ Olivier Bournez ¹ Pascal Koiran ¹ Christos Papadimitriou ¹ John Tsitsiklis ¹

1 LIP - Laboratoire de l'Informatique du Parallélisme

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.

Keywords : Stability Piecewise Linear Systems Piecewise Affine Systems Mortality Hybrid Systems Decidability Dynamical Systems

Document type :

Reports

Domain :

Computer Science [cs]

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https://hal-lara.archives-ouvertes.fr/hal-02101802
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Submitted on : Wednesday, April 17, 2019 - 9:06:39 AM
Last modification on : Saturday, September 11, 2021 - 3:19:19 AM

Deciding stability and mortality of piecewise affine dynamical systems

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Deciding stability and mortality of piecewise affine dynamical systems

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