Stochastic Approximation Results for Hybrid Inclusions

A stochastic simulator that approximates the behavior of a hybrid system given in terms of a hybrid inclusion is considered. The simulator is a stochastic discrete-time system that employs a set-valued right-hand side when approximating flows. Under mild conditions on the data defining the simulator and the hybrid system, together with a non-uniform averaging condition, it is shown that almost every sample path of each solution generated by the stochastic simulator is close to a solution of the original hybrid system on compact time domains when the step size sequence is sufficiently small and converges to zero but is not summable.