On stabilization of discrete-event processes

Concepts of stabilization of discrete-event processes are defined and investigated. An examination is made of the possibility of driving a process (under control) from arbitrary initial states to prescribed subset of the state set and then keeping it there definitely. This stabilization property is studied also with respect to open-loop processes (i.e. uncontrolled processes), and their asymptotic behavior is characterized. To this end, such well-known classical concepts of dynamics as invariant-sets and attractors are refined and characterized in the discrete-event control framework. Polynomial-time algorithms for verifying various types of attraction and for the synthesis of attractors are provided