Abstract
This paper studies state feedback control of discrete event systems where the set of control patterns is closed under union as well as intersection. It has been shown that Γ-controllability of a given predicate is a necessary and sufficient condition for the existence of a state feedback controller. However, the given predicate is not necessarily Γ-controllable. In such a case, a state feedback controller is synthesized for its supremal Γ-controllable subpredicate. An algorithm for computing the supremal Γ-controllable subpredicate has been presented under the assumption that the set of states satisfying the given predicate is finite. In this paper, we obtain the supremal Γ-controllable subpredicate where the set of states satisfying the given predicate is possibly infinite. We first present the supremal solution of a class of systems of inequalities over complete lattices. This result is then applied to obtain the supremal Γ-controllable subpredicate.
