On the existence of stationary optimal policies for the average cost control problem of linear systems with abstract state-feedback

This paper establishes conditions for the existence of optimal stationary policies for a class of long-run average cost control problems. The discrete-time system is assumed to be linear with respect to the state but the controls take an abstract state-feedback structure. The derived approach may be used to represent systems where the state is observed by the controller only through some specially structures output (no history is employed). It is shown that, if there exists an optimal-abstract policy for the discounted-cost problem, and such a policy generates an autonomous system with uniform exponential decay, then there exists an optimal stationary policy for the average cost problem. Notions of controllability and observability of linear time-varying systems are imposed.