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Deciding stability and mortality of piecewise affine dynamical systems

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.
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https://hal.inria.fr/inria-00100820
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Submitted on : Tuesday, September 26, 2006 - 2:51:37 PM
Last modification on : Friday, February 26, 2021 - 3:28:05 PM

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  • HAL Id : inria-00100820, version 1

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Vincent D. Blondel, Olivier Bournez, Pascal Koiran, Christos Papadimitriou, John N. Tsitsiklis. Deciding stability and mortality of piecewise affine dynamical systems. Theoretical Computer Science, Elsevier, 2001, 255 (1-2), pp.687-696. ⟨inria-00100820⟩

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