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.
| Original language | English |
|---|---|
| Pages (from-to) | 442-462 |
| Number of pages | 21 |
| Journal | Journal of Computer and System Sciences |
| Volume | 62 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jan 2001 |
| Externally published | Yes |
Keywords
- Decidability
- Dynamical systems
- Hybrid systems
- Mortality
- Piecewise affine systems
- Saturated linear systems
- Stability