The paper addresses discrete systems with a finite number of states which can be modelled by the state equations of a finite automaton. In contrast to traditional work, the paper is based on arithmetic representations of Boolean functions appearing on the right-hand side of the underlying finite state equations. This allows a unifying view of discrete-event systems and classical discrete-time systems. The paper focuses on the special class of arithmetically linear finite state machines. The design of feedback control using reduced-order observers is extended to this class of systems. The procedure will be illustrated by means of two examples.
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