A controllability condition for the existence of average optimal stationary policies of linear stochastic systems

This paper establishes conditions for the existence of optimal stationary policies for the long-run average cost control problem of linear stochastic systems. The control takes a general structure in such a manner that it contains, as particular case, a large number of linear control problems. The main contribution of this paper is to show that if (i) the system is controllable to the origin and (ii) a technical condition based on ε-optimal policies for the discounted problem is verified, then there exists an optimal stationary policy for the long-run average cost problem. An example is presented to illustrate the derived results.