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Some remarks on stochastic converse Lyapunov theorems
Pavel Osinenko, Grigory Yaremenko
https://arxiv.org/abs/2506.06053 https://arxi…

Some remarks on stochastic converse Lyapunov theorems
In this brief note, we investigate some constructions of Lyapunov functions for stochastic discrete-time stabilizable dynamical systems, in other words, controlled Markov chains. The main question here is whether a Lyapunov function in some statistical sense exists if the respective controlled Markov chain admits a stabilizing policy. We demonstrate some constructions extending on the classical results for deterministic systems. Some limitations of the constructed Lyapunov functions for stabili…