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.
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https://hal-lara.archives-ouvertes.fr/hal-02101802
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Vincent Blondel, Olivier Bournez, Pascal Koiran, Christos Papadimitriou, John Tsitsiklis. Deciding stability and mortality of piecewise affine dynamical systems. [Research Report] LIP RR-1999-05, Laboratoire de l'informatique du parallélisme. 1999, 2+11p. ⟨hal-02101802⟩

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