A Stability Criterion for Stochastic Hybrid Systems

This paper investigates the notion of stability for Stochastic Hybrid Systems. The uncertainty is introduced in the discrete jumps between the domains, as if we had an underlying Markov Chain. The jumps happen every fixed time T ; moreover, a result is given for the case of probabilistic dwelling times inside each domain. Unlike the more classical Hybrid Systems setting, the guards here are time-related, rather than space-related. We shall focus on vector fields describing input-less dynamical systems. Clearly, the uncertainty intrinsic to the model forces to introduce a fairly new definition of stability, which can be related to the classical Lyapunov one though. Proofs and simulations for our results are provided, as well as a motivational example from finance.