Output Feedback Control via Bisimulation of Stochastic Linear Systems

The characterization of the behavior that can be achieved by a plant when interconnected with a controller is a topic widely investigated in mathematical systems theory. In this regard, many results have been obtained for several classes of continuous systems, and also for discrete-event and hybrid systems. However, current literature is rather scant in stochastic settings. In this letter we aim to start filling this gap and provide some necessary and some sufficient checkable conditions for enforcing desired stochastic behavior, in terms of stochastic bisimulation equivalence, on discrete-time stochastic linear systems through output feedback interconnection with deterministic linear controller systems.