Deciding stability and mortality of piecewise affine dynamical systems - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Theoretical Computer Science Année : 2001

Deciding stability and mortality of piecewise affine dynamical systems

Vincent D. Blondel
  • Fonction : Auteur
Pascal Koiran
Christos Papadimitriou
  • Fonction : Auteur
John N. Tsitsiklis
  • Fonction : Auteur

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⟩
116 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More