Sampled-data event control of hybrid systems for control specifications given by predicates

We consider a hybrid system controlled by a sampled-data controller whose action is periodically time-driven, that is, the control inputs can change only at the particular time instants. We introduce a transition system as semantics of the controlled hybrid system and consider a control specification given by a predicate. First, we derive a necessary and sufficient condition for the predicate to be control-invariant and show that there always exists the supremal control-invariant subpredicate for any predicate. Finally, we propose a procedure to compute it.