Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 2:51:37 PM
Last modification on : Friday, February 26, 2021 - 3:28:05 PM


  • HAL Id : inria-00100820, version 1


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⟩



Record views