  We consider discrete-time switching systems composed of a finite family of
affine sub-dynamics. First, we recall existing results and present further
analysis on the stability problem, the existence and characterization of
compact attractors, and the relations these problems have with the joint
spectral radius of the set of matrices composing the linear part of the
subsystems. Second, we tackle the problem of providing probabilistic
certificates of stability along with the existence of forward invariant sets,
assuming no knowledge on the system data but only observing a finite number of
sampled trajectories. Some numerical examples illustrate the advantages and
limits of the proposed conditions.
