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In this paper, we develop tools to establish almost sure stability ofstochastic switched systems whose switching signal is constrained by anautomaton. After having provided the necessary generalizations of existingresults in the setting of stochastic graphs, we provide a characterization ofalmost sure stability in terms of multiple Lyapunov functions. We introduce theconcept of lifts, providing formal expansions of stochastic graphs, togetherwith the guarantee of conserving the underlying probability framework. We showhow these techniques, firstly introduced in the deterministic setting, providehierarchical methods in order to compute tight upper bounds for the almost suredecay rate. The theoretical developments are finally illustrated via anumerical example.

Almost sure Stability of Stochastic Switched Systems: Graph lifts-based Approach