Minimum second moment state for the existence of average optimal stationary policies in linear stochastic systems

This note considers the long-run aver- age cost control problem for a class of discrete-time stochastic systems. The stochastic system is assumed to be linear with respect to the state but the controls possess a general structure, possibly a nonlinear one. The main contribution of this paper is to show that the existence of a minimal second moment system state implies the existence of an optimal stationary policy for the long-run average cost problem. A numerical example illustrates the derived result.