The stability of saturated linear dynamical systems is undecidable

Blondel, Vincent;Bournez, O;Koiran, P;Tsitsiklis, John
(2001) Journal of Computer and System Sciences — Vol. 62, n° 3, p. 442-462 (2001)

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Authors
  • Blondel, Vincentorcid-logoUCLouvain
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  • Bournez, O
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  • Koiran, P
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  • Tsitsiklis, John
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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 3. We also describe some consequences of our results on the possible dynamics of such systems. (C) 2001 Academic Press.
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Blondel, V., Bournez, O., Koiran, P., & Tsitsiklis, J. (2001). The stability of saturated linear dynamical systems is undecidable. Journal of Computer and System Sciences, 62(3), 442-462. https://doi.org/10.1006/jcss.2000.1737 (Original work published 2001)