Controllability and observability in the state-feedback control of discrete-event systems

A discrete-event system (DES) is described by a state-transition model. By disabling and enabling controllable events according to a rule based on partial information about the current state of the system, a static state-feedback controller synthesizes a predicate specifying states reachable from the initial state in the controlled system. Concepts of controllable predicate and observable predicate are introduced. It is shown that a predicate can be synthesized by a static state-feedback controller utilizing only partial state information if and only if the predicate is both controllable and observable. Some general results are presented for a state-variable model of a controlled DES