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Article Dans Une Revue Theoretical Computer Science Année : 2001

Deciding stability and mortality of piecewise affine dynamical systems

Résumé

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.

Domaines

Autre [cs.OH]

Dates et versions

inria-00100820 , version 1 (26-09-2006)

Identifiants

Citer

Vincent D. Blondel, Olivier Bournez, Pascal Koiran, Christos Papadimitriou, John N. Tsitsiklis. Deciding stability and mortality of piecewise affine dynamical systems. Theoretical Computer Science, 2001, 255 (1-2), pp.687-696. ⟨10.1016/S0304-3975(00)00399-6⟩. ⟨inria-00100820⟩
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