  We propose an extension of the theory of control sets to the case of inputs
satisfying a dwell-time constraint. Although the class of such inputs is not
closed under concatenation, we propose a suitably modified definition of
control sets that allows to recover some important properties known in the
concatenable case. In particular we apply the control set construction to
dwell-time linear switched systems, characterizing their maximal Lyapunov
exponent looking only at trajectories whose angular component is periodic. We
also use such a construction to characterize supports of invariant measures for
random switched systems with dwell-time constraints.
