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In this paper, we consider the problem of probabilistic stability analysis ofa subclass of Stochastic Hybrid Systems, namely, Polyhedral ProbabilisticHybrid Systems (PPHS), where the flow dynamics is given by a polyhedralinclusion, the discrete switching between modes happens probabilistically atthe boundaries of their invariant regions and the continuous state is not resetduring switching. We present an abstraction-based analysis framework thatconsists of constructing a finite Markov Decision Processes (MDP) such thatverification of certain property on the finite MDP ensures the satisfaction ofprobabilistic stability on the PPHS. Further, we present a polynomial-timealgorithm for verifying the corresponding property on the MDP. Our experimentalanalysis demonstrates the feasibility of the approach in successfully verifyingprobabilistic stability on PPHS of various dimensions and sizes.

Abstraction-based Probabilistic Stability Analysis of Polyhedral Probabilistic Hybrid Systems