A converse Lyapunov theorem for asymptotic stability in probability
نویسندگان
چکیده
A converse Lyapunov theorem is established for discrete-time stochastic systems with non-unique solutions. In order to prove the result, mild regularity conditions are imposed on the set-valued mapping that characterizes the update of the system state. It is shown that global asymptotic stability in probability implies the existence of a continuous Lyapunov function, smooth outside of the attractor, that decreases in expected value along solutions. Additional results on the robustness of global asymptotic stability in probability are used to construct a Lyapunov function with the desired regularity properties.
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