A Lyapunov theorem certifying global weak reachability for stochastic difference inclusions with random inputs

In this paper, a Lyapunov condition certifying global weak reachability of a compact set is given for stochastic, set-valued, discrete-time systems. With respect to such systems, under mild regularity assumptions, it is shown that the existence of a lower semicontinuous function that decreases in expected value for at least one measurable selection from the set-valued mapping outside a compact set is a sufficient condition for global weak reachability of such a set.