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We introduce new sufficient conditions for verifying stability and recurrenceproperties in singularly perturbed stochastic hybrid dynamical systems.Specifically, we focus on hybrid systems with deterministic continuous-timedynamics that exhibit multiple time scales and are modeled by constraineddifferential inclusions, as well as discrete-time dynamics modeled byconstrained difference inclusions with random inputs. By assuming regularityand causality of the dynamics and their solutions, respectively, we propose asuitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Fosterfunctions that can certify stability and recurrence using simpler functionsrelated to the slow and fast dynamics of the system. We establish the stabilityproperties with respect to compact sets, while the recurrence properties arestudied only for open sets.

Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions