Output stabilizability of discrete-event dynamic systems

The authors investigate the problem of designing stabilizing feedback compensators for discrete-event dynamic systems (DEDS) modeled as finite-state automata in which some transition events are controllable and some events are observed. The problem of output stabilization is defined as the construction of a compensator such that all state trajectories in the closed-loop system go through a given set E infinitely often. The authors also define a stronger notion of output stabilizability which requires that the state not only pass through E infinitely often but that the set of instants when the state is in E and one knows it is in E is also infinite. Necessary and sufficient conditions are presented for both notions. The authors also introduce and characterize a notion of resiliency that corresponds to the system being able to recover from observation errors. In addition, they provide some general bounds for the algorithms considered and discuss several conditions under which far smaller bounds can be achieved