In a real-time system, when the execution of a task is preempted by another task, the interrupted task falls into a blocked state. Since its re-execution begins from the interrupted point generally, the task's timer containing the remaining time until its completion should be maintained in the blocked state. This is the reason for introducing the notion of memorable events in this paper. We present a new timed discrete event model (TDEM) that adds the memorable events to the TDEM framework of Brandin and Wonham (1994). Using supervisory control theory upon the proposed TDEM, we analyze the schedulability of preemptable periodic and sporadic tasks executing on a uniprocessor.

In networked control systems, uncontrollable events may unexpectedly occur in a plant before a proper control action is applied to the plant due to communication delays. In the area of supervisory control of discrete event systems, Park and Cho [5] proposed the notion of delay-nonconflictingness for the existence of a supervisor achieving a given language specification under communication delays. In this paper, we present the algebraic properties of delay-nonconflicting languages which are necessary for solving supervisor synthesis problems under communication delays. Specifically, we show that the class of prefix-closed and delay-nonconflicting languages is closed under intersection, which leads to the existence of a unique infimal prefix-closed and delay-nonconflicting superlanguage of a given language specification.