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The stability of saturated linear dynamical systems is undecidable

Abstract : We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only for point-to-point properties. We prove these properties undecidable for saturated linear dynamical systems, and for continuous piecewise affine dynamical systems in dimension three. We also describe some consequences of our results on the possible dynamics of such systems.
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Submitted on : Tuesday, September 26, 2006 - 2:52:56 PM
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  • HAL Id : inria-00100924, version 1


Vincent D. Blondel, Olivier Bournez, Pascal Koiran, John N. Tsitsiklis. The stability of saturated linear dynamical systems is undecidable. Journal of Computer and System Sciences, Elsevier, 2001, 62 (3), pp.442-462. ⟨inria-00100924⟩



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