  Can we conclude the stability of an unknown dynamical system from the
knowledge of a finite number of snapshots of trajectories? We tackle this
black-box problem for switched linear systems. We show that, for any given
random set of observations, one can give probabilistic stability guarantees.
The probabilistic nature of these guarantees implies a trade-off between their
quality and the desired level of confidence. We provide an explicit way of
computing the best stability-like guarantee, as a function of both the number
of observations and the required level of confidence. Our proof techniques rely
on geometrical analysis, chance-constrained optimization, and stability
analysis tools for switched systems, including the joint spectral radius.
