Lyapunov conditions certifying stability and recurrence for a class of stochastic hybrid systems

Lyapunov-based conditions for stability and recurrence are presented for a class of stochastic hybrid systems where solutions are not necessarily unique, either due to nontrivial overlap of the flow and jump sets, a set-valued jump map, or a set-valued flow map. Randomness enters exclusively through the jump map, yet the framework covers systems with spontaneous transitions. Regularity conditions are given that guarantee the existence of random solutions and robustness of the Lyapunov conditions.