Markov set-chains as abstractions of stochastic hybrid systems

Abstract. The objective of this study is to introduce an abstraction procedure that applies to a general class of dynamical systems, that is to discrete-time stochastic hybrid systems (dt-SHS). The procedure ab-stracts the original dt-SHS into a Markov set-chain (MSC) in two steps. First, a Markov chain (MC) is obtained by partitioning the hybrid state space, according to a controllable parameter, into non-overlapping do-mains and computing transition probabilities for these domains accord-ing to the dynamics of the dt-SHS. Second, explicit error bounds for the abstraction that depend on the above parameter are derived, and are associated to the computed transition probabilities of the MC, thus ob-taining a MSC. We show that one can arbitrarily increase the accuracy of the abstraction by tuning the controllable parameter, albeit at an in-crease of the cardinality of the MSC. Resorting to a number of results from the MSC literature allows the analysis of the dynamics of the orig-inal dt-SHS. In the present work, the asymptotic behavior of the dt-SHS dynamics is assessed within the abstracted framework.