Linear discrete-event systems and robust servomechanism problem

Linear discrete-event systems are studied. Reachability, observability, controllability, constructibility, stabilizability and detectability of such systems are investigated. Stability of linear discrete-event systems is also considered. It is shown that a stabilizable and detectable linear time-invariant discrete-event system can be stabilized by a linear time-invariant discrete-event controller. A robust servomechanism problem for linear discrete-event systems is also discussed. The necessary and sufficient conditions for the existence of a solution to this problem are presented.