Stationary policies for the second moment stability in a class of stochastic systems

This paper presents a study on the uniform second moment stability for a class of stochastic control system. The main result states that the existence of the long-run average cost under a stationary policy is equivalent to the uniform second moment stability of the corresponding stochastic control system. To illustrate the result, a numerical example is developed to verify the uniform second moment stability of a simultaneous state-feedback control system.