  We present a data-driven framework based on Lyapunov theory to provide
stability guarantees for a family of hybrid systems. In particular, we are
interested in the asymptotic stability of switching linear systems whose
switching sequence is constrained by labeled graphs, namely constrained
switching linear systems. In order to do so, we provide chance-constrained
bounds on stability guarantees, that can be obtained from a finite number of
noisy observations.
  We first present a method providing stability guarantees from sampled
trajectories in the hybrid state-space of the system. We then study the harder
situation where one only observes the continuous part of the hybrid states. We
show that in this case, one may still obtain formal chance-constrained
stability guarantees. For this latter result we provide a new upper bound of
general interest, also for model-based stability analysis
