M -controllable subpredicates arising in state feed back control of discrete event systems

This paper studies M -controllable subpredicates of a given predicate, which arise in state feedback control of discrete event systems under partial observations. First, the notion of strong M -controllability of predicates, which is a stronger version of M -controllability, is introduced. Then it is shown that there always exists the supremal strongly M -controllable subpredicate of a given predicate. Also, it is proved that the supremal strongly M -controllable subpredicate is larger than the supremal controllable and normal subpredicate obtained by Li. However, the supremal strongly M -controllable subpredicate is not a maximal M -controllable subpredicate in general. A sufficient condition for an obtained M -controllable subpredicate to be a maximal one is presented.